A269871 Indices of square pyramidal numbers (A000330) that are the sum of 4 but no fewer nonzero squares.

5, 14, 21, 30, 37, 39, 40, 46, 53, 62, 69, 78, 85, 94, 101, 103, 104, 110, 117, 126, 133, 142, 149, 158, 159, 160, 165, 167, 168, 174, 181, 190, 197, 206, 213, 222, 229, 231, 232, 238, 245, 254, 261, 270, 277, 286, 293, 295, 296, 302, 309, 318, 325, 334, 341, 350, 357

Offset

1,1

Comments

In other words, integers n such that equation 1^2 + 2^2 + ... + n^2 = x^2 + y^2 + z^2 where x, y and z are integers is not soluble.

Corresponding square pyramidal numbers are 55, 1015, 3311, 9455, 17575, 20540, 22140, 33511, 51039, 81375, 111895, 161239, 208335, 281295, 348551, 369564, ...

Initial terms of first differences of this sequence are 9, 7, 9, 7, 2, 1, 6, 7, 9, 7, 9, 7, 9, 7, 2, 1, 6, 7, 9, 7, 9, 7, ...

Links

Table of n, a(n) for n=1..57.

Example

5 is a term because A000330(5) = 55 and the equation 55 = x^2 + y^2 + z^2 where x, y, z are integers is not soluble.

Prog

(PARI) isA004215(n) = { my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) ; fouri *= 4 ; ) ; return(0) ; }
for(n=0, 1e3, if(isA004215(n*(n+1)*(2*n+1)/6), print1(n, ", ")));

Crossrefs

Cf. A000330, A004215.

Sequence in context: A071317 A167201 A336145 * A323732 A048769 A190514

Adjacent sequences: A269868 A269869 A269870 * A269872 A269873 A269874

Keyword

nonn

Author

Altug Alkan, Mar 06 2016

Status

approved