The number representing the current year is both divisible by 7 and so is the sum of its digits. This feature allows me to take the liberty and to call it
a SEPTEMVIRAL year, or shortly SY.
Now, the puzzle:
What span of 1000 years (from X to X+999) containing 2023, provides the highest quantity of SYs?
clearvars,clc
mx=0;
for st=1924:2023
r=st:st+999;
f=find(mod(r,7)==0 & mod(sod(r),7)==0);
ct=length(f);
disp([st st+999 ct])
if ct>mx
mx=ct;
end
end
for st=1924:2023
r=st:st+999;
f=find(mod(r,7)==0 & mod(sod(r),7)==0);
ct=length(f);
if ct==mx
fprintf('%5d%5d%5d\n',st, st+999 ,ct)
fprintf('%5d',r(f));
fprintf('\n\n')
end
end
where
sod is
function sd = sod(n0)
for i=1:length(n0)
n=n0(i);
dgts=num2str(n) ;
sd(i)=sum(dgts-48);
end
end
which is dependent on the ASCII value of '0' being decimal 48.
The program finds the following counts for the given thousand years:
1924 2923 21
1925 2924 21
1926 2925 21
1927 2926 21
1928 2927 21
1929 2928 21
1930 2929 21
1931 2930 21
1932 2931 21
1933 2932 21
1934 2933 21
1935 2934 21
1936 2935 21
1937 2936 21
1938 2937 21
1939 2938 21
1940 2939 21
1941 2940 21
1942 2941 21
1943 2942 21
1944 2943 21
1945 2944 21
1946 2945 21
1947 2946 21
1948 2947 21
1949 2948 21
1950 2949 21
1951 2950 21
1952 2951 21
1953 2952 21
1954 2953 21
1955 2954 21
1956 2955 21
1957 2956 21
1958 2957 21
1959 2958 21
1960 2959 21
1961 2960 21
1962 2961 21
1963 2962 21
1964 2963 21
1965 2964 21
1966 2965 21
1967 2966 21
1968 2967 21
1969 2968 21
1970 2969 21
1971 2970 21
1972 2971 21
1973 2972 21
1974 2973 21
1975 2974 20
1976 2975 20
1977 2976 20
1978 2977 20
1979 2978 20
1980 2979 20
1981 2980 20
1982 2981 20
1983 2982 21
1984 2983 21
1985 2984 21
1986 2985 21
1987 2986 21
1988 2987 21
1989 2988 21
1990 2989 22
1991 2990 22
1992 2991 22
1993 2992 22
1994 2993 22
1995 2994 22
1996 2995 22
1997 2996 22
1998 2997 22
1999 2998 22
2000 2999 22
2001 3000 22
2002 3001 22
2003 3002 22
2004 3003 22
2005 3004 22
2006 3005 22
2007 3006 22
2008 3007 22
2009 3008 22
2010 3009 22
2011 3010 22
2012 3011 22
2013 3012 22
2014 3013 22
2015 3014 22
2016 3015 22
2017 3016 22
2018 3017 22
2019 3018 22
2020 3019 22
2021 3020 22
2022 3021 22
2023 3022 22
The largest count found was 22. All these thousand-year periods contain the same set of 22, which span 967 years:
1990 2989 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1991 2990 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1992 2991 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1993 2992 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1994 2993 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1995 2994 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1996 2995 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1997 2996 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1998 2997 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
1999 2998 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2000 2999 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2001 3000 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2002 3001 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2003 3002 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2004 3003 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2005 3004 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2006 3005 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2007 3006 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2008 3007 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2009 3008 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2010 3009 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2011 3010 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2012 3011 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2013 3012 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2014 3013 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2015 3014 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2016 3015 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2017 3016 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2018 3017 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2019 3018 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2020 3019 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2021 3020 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2022 3021 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
2023 3022 22
2023 2093 2156 2212 2219 2282 2289 2345 2401 2408 2471 2478 2534 2660 2667 2723 2793 2856 2912 2919 2982 2989
>>
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Posted by Charlie
on 2023-04-22 20:30:44 |
computer solution