What prime members will follow:
3,13,37.......?
Provide your reasoning.
You skip one prime (2), to use the second prime (3) as the first member of the sequence.
Then you skip 3 primes to get to the 6th prime, 13.
Then you skip 5 primes to get to the 12th prime, 37.
Next, you would skip 7 primes to get to the 20th prime, 71, etc.:
Tabulated with ordinal number of the prime, the first few primes are:
2 3
6 13
12 37
20 71
30 113
42 181
56 263
72 359
90 463
110 601
132 743
156 911
182 1091
210 1291
240 1511
272 1747
306 2017
342 2297
380 2617
420 2903
462 3271
506 3617
552 4003
600 4409
Laid out it looks like
3, 13, 37, 71, 113, 181, 263, 359, 463, 601, 743, 911, 1091, 1291, 1511, 1747, 2017, 2297, 2617, 2903, 3271, 3617, 4003, 4409, 4831, 5297, 5743, ...
Tabulated via the MATLAB program:
pr=primes(10000);
ansptr=0;
ptr=0;
for skp=2:2:55
ptr=ptr+skp;
ansptr=ansptr+1;
answ(ansptr)=pr(ptr);
fprintf(' %d %d\n',ptr,pr(ptr))
end
fprintf('%d, ',answ)
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Posted by Charlie
on 2020-09-22 10:58:39 |
one possible take on it