All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Triplets cubed (Posted on 2020-10-04) Difficulty: 2 of 5
Let y(n) represent sum of digits of n3.

For 10<n<999 list all the triplets (n,n+1,n+2) such that y(n),y(n+1),y(n+2)
are three successive integers
a.in any order
b.corresponding to n,n+1,n+2.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
part b Comment 3 of 3 |
Part b
When the y values must be in order, there are 38 of them (121 for 'a')
(code is below)
(Part a solved by un-commenting one line of code and comment out one other line.)

14 15 16
23 24 25
41 42 43
71 72 73
77 78 79
86 87 88
161 162 163
224 225 226
242 243 244
254 255 256
272 273 274
296 297 298
302 303 304
305 306 307
314 315 316
350 351 352
425 426 427
431 432 433
437 438 439
455 456 457
473 474 475
497 498 499
596 597 598
602 603 604
611 612 613
635 636 637
665 666 667
677 678 679
713 714 715
764 765 766
836 837 838
851 852 853
872 873 874
881 882 883
896 897 898
947 948 949
950 951 952
962 963 964
38

def sod(n):
    """ Input an integer.  Returns the Sum of the Digits  """
    aList = list(str(n))
    ans = 0
    for c in aList:
        ans = ans + int(c)
    return ans

def isTriplet(a,b,c,inOrder = False):
    if inOrder:
        l= ([a,b,c])
    else:
        l= sorted([a,b,c])
    if l[1]-l[0] == 1 and l[2]-l[1] == 1:
        return True
    return False
    

sumOfCubes = []
biggestN = 1000
for n in range(biggestN):
    sumOfCubes.append(sod(n**3))
count = 0
for i in range(12,biggestN):
    if isTriplet(sumOfCubes[i-2],sumOfCubes[i-1],sumOfCubes[i],True):
#    if isTriplet(sumOfCubes[i-2],sumOfCubes[i-1],sumOfCubes[i]):
        count += 1
        print(i-2,i-1,i )
        
print(count)

Edited on October 4, 2020, 12:10 pm
  Posted by Larry on 2020-10-04 12:07:26

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (2)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information