A265150 a(1) = 10, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.

10, 24, 336, 400, 689, 5876, 7556, 8249, 53284, 335556, 4512400, 25092921, 165947209, 496186596, 3891489129, 6897736129, 10128495225, 18547234816, 81770476100, 203672467856, 909690622025, 6063906517681, 14045408555225, 50912872680100, 145763131189824, 180798422222500

Offset: 1

Author

Robert G. Wilson v, Dec 02 2015

Keywords

• nonn
• base

Examples

			a(3) is 336 since it is the least number greater than a(2)=24 which concatenated with 24 forms a perfect square, i.e., 24336 = 156^2.
		

Crossrefs

Cf. A090566, A265147, A265148, A265149, A265151, A265152, A265153, A265154, A265155.

Programs

Mathematica

f[n_] := Block[{x = n, d = 1 + Floor@ Log10@ n}, q = (Floor@ Sqrt[(10^d + 1) x] + 1)^2; If[q < (10^d) (x + 1), Mod[q, 10^d], Mod[(Floor@ Sqrt[(10^d)(10x + 1) - 1] + 1)^2, 10^(d + 1)] ]]; NestList[f, 10, 25] (* after the algorithm of David W. Wilson in A090566 *)