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

1,1

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

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 *)

Prog

(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

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).

Sequence in context: A345186 A251368 A366516 * A065695 A204368 A114131

Adjacent sequences: A224480 A224481 A224482 * A224484 A224485 A224486

Keyword

nonn,easy

Author

Vincenzo Librandi, May 08 2013

Status

approved