A329386 Numbers k such that k + A055012(k) is a square.

17, 104, 216, 260, 342, 392, 500, 518, 540, 590, 746, 830, 848, 1008, 1073, 1077, 1166, 1169, 1233, 1313, 1694, 1784, 1835, 1962, 1998, 2252, 2420, 2897, 3006, 3047, 3087, 3302, 3762, 4316, 4416, 4424, 4706, 4928, 5031, 5126, 5273, 5435, 6137, 6399, 6813, 7134, 7259, 7442, 7449, 7655, 7895, 7992

Offset: 1

Author

Will Gosnell and Robert Israel, Nov 12 2019

Keywords

• nonn
• base

Examples

			a(3)=216 is a term because 216 + 2^3 + 1^3 + 6^3 = 441 = 21^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055012, A329179.

Programs

Magma

[k:k in [1..8000]|IsSquare(k+&+[c^3: c in Intseq(k)])]; // Marius A. Burtea, Nov 12 2019

Maple

filter:= proc(n) local t;
  issqr( n + add(t^3,t=convert(n,base,10)));
end proc:
select(filter, [$1..10000]);

PARI

A055012(n)=sum(i=1, #n=digits(n), n[i]^3)
is(n)=issquare(n + A055012(n)) \\ Charles R Greathouse IV, Jun 10 2020