A362069 Numbers k such that k+digitsum(k^2) is a square.

0, 17, 62, 71, 117, 125, 197, 206, 296, 297, 305, 413, 414, 557, 558, 692, 702, 711, 863, 864, 872, 873, 1062, 1070, 1071, 1268, 1493, 1502, 1727, 1736, 1737, 1745, 1998, 2006, 2267, 2276, 2285, 2564, 2565, 2573, 2879, 2888, 2889, 3221, 3222

Offset: 1

Author

Alexandru Petrescu, May 17 2023

Keywords

• nonn
• easy
• base

Comments

Conjecture: there are infinitely many pairs of consecutive terms. Example: (296,297); (413,414); (863,864).

Examples

			k=17 is a term because k^2=289 and 17+2+8+9=36=6^2.
		

Crossrefs

Cf. A004159, A066564.

Programs

Mathematica

Select[Range[0, 3300], IntegerQ[Sqrt[# + Plus @@ IntegerDigits[#^2]]] &] (* Amiram Eldar, May 18 2023 *)

PARI

isok(k)=issquare(k+sumdigits(k^2))