A329386 -id:A329386 - cp's OEIS frontend

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

Will Gosnell and Robert Israel, Nov 07 2019

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

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

Cf. A010052, A258881, A329386.

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

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

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

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

A338235 Numbers k such that k + the sum of the 4th powers of the decimal digits of k is a square.

Original entry on oeis.org

20, 47, 104, 113, 228, 255, 333, 544, 632, 743, 1054, 1122, 1518, 1762, 1901, 2071, 3617, 4317, 4432, 4456, 4513, 4557, 4727, 4927, 5000, 5058, 5080, 5173, 5473, 5847, 6047, 6767, 6832, 7247, 7408, 7453, 7487, 7518, 7921, 7997, 8127, 8958, 9208, 9487, 10917

Offset: 1

Will Gosnell, Jan 30 2021

			20 is a member since 2^4 + 0^4 + 20 = 6^2,
47 is a member since 4^4 + 7^4 + 47 = 52^2,
104 is a member since 1^4 + 0^4 + 4^4 = 104 = 19^2,
113 is a member since 1^4 + 1^4 + 3^4 + 113 = 14^2.

Cf. A055013, A329179, A329386.

filter:= proc(n) local L,k;
  issqr(n + add(t^4, t=convert(n,base,10)))
end proc:
select(filter, [$1..20000]); # Robert Israel, Jan 30 2021

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python