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a(3) is 89 since it is the least number greater than 44, a(2), =44 which concatenated with 44 forms a perfect square, i.e.; , 4489 = 67^2.

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, 14, 24] (* after the algorithm of _David W. Wilson _ in A090566 *)

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a(1) = 14, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.

a(3) is 89 since it is the least number greater than 44, a(2), which concatenated with 44 forms a perfect square, i.e.; 4489 = 67^2.

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, 14, 24] (* after the algorithm of David W. Wilson in A090566 *)

Cf. A090566, A265147, A265148, A265149, A265150, A265151, A265153, A265154, A265155.

nonn,changed,base

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allocated for Robert G a(1) = 14, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square. Wilson v

14, 44, 89, 401, 956, 6649, 17796, 58596, 432489, 4211044, 22847241, 34268944, 85740489, 530152900, 718608036, 3266783209, 33250749225, 96733442161, 617288020224, 5959324297569, 20015258667081, 123104551223296, 420105398760804, 552382701059344, 967075372931216

1,1

a(3) is 89 since it is the least number greater than 44, a(2), which concatenated with 44 forms a perfect square, i.e.; 4489 = 67^2.

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, 14, 24] (* after the algorithm of David W. Wilson in A090566 *)

Cf. A090566, A265147, A265148, A265149, A265150, A265151, A265153, A265154, A265155.

allocated

nonn

Robert G. Wilson v, Dec 02 2015

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allocated for Robert G. Wilson v

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approved