A224483 Numbers which are the sum of two positive cubes and divisible by 29.

6119, 6293, 6641, 7163, 7859, 8729, 9773, 10991, 12383, 13949, 15689, 17603, 19691, 21953, 48778, 48952, 49474, 50344, 51562, 53128, 55042, 57304, 59914, 62872, 66178, 69832, 73834, 78184, 82882, 87928, 93322, 99064, 105154

Offset: 1

Author

Vincenzo Librandi, May 08 2013

Keywords

• nonn
• easy

Comments

If 12*h-2523 is a square then some values of 29*h are in this sequence.

It is easy to verify that h is of the form 3*m^2-9*m+217, and therefore 29*(3*m^2-9*m+217) = (16-m)^3+(m+13)^3. [Bruno Berselli, May 10 2013]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. numbers which are the sum of two positive cubes and divisible by k: A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A102658 (k=31), A102618 (k=37).

Programs

Magma

[n: n in [2..2*10^5] | exists{i: i in [1..Iroot(n-1,3)] | IsPower(n-i^3,3) and IsZero(n mod 29)}]; // Bruno Berselli, May 10 2013

Mathematica

upto[n_] := Block[{t}, Union@Reap[ Do[If[Mod[t = x^3 + y^3, 29] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[106000] (* Giovanni Resta, Jun 12 2020 *)