A061230 Numbers k such that k + the reversal of k is a square.

0, 2, 8, 29, 38, 47, 56, 65, 74, 83, 92, 110, 143, 164, 198, 242, 263, 297, 341, 362, 396, 440, 461, 495, 560, 594, 693, 792, 891, 990, 10100, 10148, 10340, 10395, 10403, 10683, 10908, 10980, 11138, 11330, 11385, 11673, 11970, 12128, 12320, 12375

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava)

Example

8 is a term as 8 + 8 = 16 = 4^2.
56 is a term as 56 + 65 = 121 = 11^2.

Maple

digrev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
select(t -> issqr(t+digrev(t)), [$0..20000]); # Robert Israel, May 04 2015

Mathematica

Select[Range[0, 15000], IntegerQ[Sqrt[#+FromDigits[Reverse[ IntegerDigits[#]]]]]&]  (* Harvey P. Dale, Apr 18 2011 *)

Prog

(PARI) isok(n) = issquare(n + fromdigits(Vecrev(digits(n)))); \\ Michel Marcus, Aug 04 2019
(Python)
from math import isqrt
def issquare(n): return isqrt(n)**2 == n
def ok(n): return issquare(n + int(str(n)[::-1]))
print([k for k in range(12376) if ok(k)]) # Michael S. Branicky, Dec 09 2022

Crossrefs

Cf. A056964, A061231.

Cf. A359011 (for squares).

Sequence in context: A330211 A216785 A261559 * A241627 A293169 A306847

Adjacent sequences: A061227 A061228 A061229 * A061231 A061232 A061233

Keyword

nonn,base

Author

Amarnath Murthy, Apr 23 2001

Extensions

Corrected and extended by Patrick De Geest, May 28 2001

Edited by N. J. A. Sloane, Jul 24 2009

Status

approved