A329179 Numbers k such that A258881(k) is a square.

0, 23, 36, 52, 71, 80, 104, 137, 143, 154, 377, 443, 479, 533, 823, 963, 977, 1013, 1125, 1204, 1284, 1334, 1493, 1624, 1769, 1786, 1997, 2047, 2110, 2228, 2260, 2427, 2508, 2577, 2707, 2740, 3121, 3174, 3223, 3407, 3440, 3477, 3526, 3644, 3745, 3828, 3860, 4027, 4079, 4163, 4314, 4384, 4518

Offset: 1

Author

Will Gosnell and Robert Israel, Nov 07 2019

Keywords

• base
• nonn

Examples

			a(3) = 36 is a member of the sequence because 36 + 3^2 + 6^2 = 81 = 9^2.
		

Links

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

Crossrefs

Cf. A010052, A258881, A329386.

Programs

Maple

filter:= n -> issqr(n + convert(map(`^`,convert(n,base,10),2),`+`)):
select(filter, [$0..10^4]);

Mathematica

Select[Range[0,5000],IntegerQ[Sqrt[#+Total[IntegerDigits[#]^2]]]&] (* Harvey P. Dale, Jan 01 2022 *)

PARI

isok(k) = issquare(k+norml2(digits(k))); \\ Michel Marcus, Jan 31 2021

Python

from sympy.ntheory.primetest import is_square
def ssd(n): return sum(int(d)**2 for d in str(n))
def ok(n): return is_square(n + ssd(n))
def aupto(limit): return [m for m in range(limit+1) if ok(m)]
print(aupto(4000)) # Michael S. Branicky, Jan 30 2021