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

%I A329179 #23 Jan 01 2022 19:04:26
%S A329179 0,23,36,52,71,80,104,137,143,154,377,443,479,533,823,963,977,1013,
%T A329179 1125,1204,1284,1334,1493,1624,1769,1786,1997,2047,2110,2228,2260,
%U A329179 2427,2508,2577,2707,2740,3121,3174,3223,3407,3440,3477,3526,3644,3745,3828,3860,4027,4079,4163,4314,4384,4518
%N A329179 Numbers k such that A258881(k) is a square.
%H A329179 Robert Israel, <a href="/A329179/b329179.txt">Table of n, a(n) for n = 1..10000</a>
%e A329179 a(3) = 36 is a member of the sequence because 36 + 3^2 + 6^2 = 81 = 9^2.
%p A329179 filter:= n -> issqr(n + convert(map(`^`,convert(n,base,10),2),`+`)):
%p A329179 select(filter, [$0..10^4]);
%t A329179 Select[Range[0,5000],IntegerQ[Sqrt[#+Total[IntegerDigits[#]^2]]]&] (* _Harvey P. Dale_, Jan 01 2022 *)
%o A329179 (Python)
%o A329179 from sympy.ntheory.primetest import is_square
%o A329179 def ssd(n): return sum(int(d)**2 for d in str(n))
%o A329179 def ok(n): return is_square(n + ssd(n))
%o A329179 def aupto(limit): return [m for m in range(limit+1) if ok(m)]
%o A329179 print(aupto(4000)) # _Michael S. Branicky_, Jan 30 2021
%o A329179 (PARI) isok(k) = issquare(k+norml2(digits(k))); \\ _Michel Marcus_, Jan 31 2021
%Y A329179 Cf. A010052, A258881, A329386.
%K A329179 base,nonn
%O A329179 1,2
%A A329179 _Will Gosnell_ and _Robert Israel_, Nov 07 2019