A274794 Numbers n such that n^3 is the sum of two triangular numbers in exactly one way.

0, 1, 3, 4, 7, 9, 10, 19, 24, 25, 34, 37, 39, 42, 49, 54, 55, 72, 73, 78, 85, 87, 93, 94, 102, 108, 109, 118, 138, 142, 147, 157, 160, 165, 168, 175, 192, 195, 202, 210, 214, 220, 228, 232, 243, 247, 249, 250, 252, 253, 258, 267, 273, 274, 279, 289, 297, 312, 333

Offset

1,3

Comments

A115104 is a subsequence. Terms such that 4*n^3 + 1 is not prime are 24, 337, 457, 750, 840, 1015, ...

Links

Table of n, a(n) for n=1..59.

Example

3 is a term because 3^3 = 27 = 6 + 21.

Mathematica

Select[Range@ 333, Length[PowersRepresentations[4 #^3 + 1, 2, 2]] == 1 &] (* after Ant King at A052343, or *)
nn = 20; t = (#^2 + #)/2 & /@ Range[0, nn^3]; Select[Range[0, nn], Function[n, Count[Transpose@ {#, n^3 - #} &@ Range[0, Floor[n^3/2]], k_ /; Times @@ Boole@ Map[MemberQ[t, #] &, k] == 1] == 1]] (* Michael De Vlieger, Jul 07 2016 *)

Prog

(PARI) a052343(n) = sum(i=0, (sqrtint(4*n + 1) - 1)\2, issquare(n - i - i^2));
lista(nn) = for(n=0, nn, if(a052343(n^3) == 1, print1(n, ", ")));

Crossrefs

Cf. A000217, A000578, A020756, A052343, A115104, A119345.

Sequence in context: A212013 A256761 A039579 * A115104 A095043 A019990

Adjacent sequences: A274791 A274792 A274793 * A274795 A274796 A274797

Keyword

nonn

Author

Altug Alkan, Jul 07 2016

Status

approved