A265149 a(1) = 8, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.

8, 41, 209, 764, 5225, 8441, 9344, 63761, 82201, 477264, 3191044, 4038489, 34656049, 61233321, 271005625, 3465072801, 36565416324, 83511106624, 222222321476, 425286636356, 2743260628100, 9534841632400, 33984728488004, 128198574830929, 741089622057984, 5579432351776489

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Example

a(3) is 209 since it is the least number greater than a(2)=41 which concatenated with 41 forms a perfect square, i.e., 41209 = 203^2.

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, 8, 25] (* after the algorithm of David W. Wilson in A090566 *)

Crossrefs

Cf. A090566, A265147, A265148, A265150, A265151, A265152, A265153, A265154, A265155.

Sequence in context: A026968 A026978 A037577 * A209822 A051737 A209841

Adjacent sequences: A265146 A265147 A265148 * A265150 A265151 A265152

Keyword

nonn,base

Author

Robert G. Wilson v, Dec 02 2015

Status

approved