A329179 - OEIS

%I #23 Jan 01 2022 19:04:26

%S 0,23,36,52,71,80,104,137,143,154,377,443,479,533,823,963,977,1013,

%T 1125,1204,1284,1334,1493,1624,1769,1786,1997,2047,2110,2228,2260,

%U 2427,2508,2577,2707,2740,3121,3174,3223,3407,3440,3477,3526,3644,3745,3828,3860,4027,4079,4163,4314,4384,4518

%N Numbers k such that A258881(k) is a square.

%H Robert Israel, <a href="/A329179/b329179.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= n -> issqr(n + convert(map(`^`,convert(n,base,10),2),`+`)):

%p select(filter, [$0..10^4]);

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

%o (Python)

%o from sympy.ntheory.primetest import is_square

%o def ssd(n): return sum(int(d)**2 for d in str(n))

%o def ok(n): return is_square(n + ssd(n))

%o def aupto(limit): return [m for m in range(limit+1) if ok(m)]

%o print(aupto(4000)) # _Michael S. Branicky_, Jan 30 2021

%o (PARI) isok(k) = issquare(k+norml2(digits(k))); \\ _Michel Marcus_, Jan 31 2021

%Y Cf. A010052, A258881, A329386.

%K base,nonn

%O 1,2

%A _Will Gosnell_ and _Robert Israel_, Nov 07 2019