A243091 Least number k > n such that n concatenated with k is a perfect square.

1, 6, 5, 6, 9, 29, 25, 29, 41, 61, 24, 56, 25, 69, 44, 21, 81, 64, 49, 36, 25, 316, 201, 104, 336, 281, 244, 225, 224, 241, 276, 36, 49, 64, 81, 344, 100, 249, 44, 69, 96, 209, 436, 56, 89, 369, 225, 61, 400, 284, 176, 84, 441, 361, 76, 225, 169, 76, 564, 536, 84, 504, 500, 504, 516, 536

Offset

0,2

Comments

Records occur at: 0, 1, 4, 5, 8, 9, 13, 16, 21, 24, 35, 42, 52, 58, 67, 75, 80, ..., . - Robert G. Wilson v, Nov 23 2015

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Example

a(1) = 6 since 6>1 and 16 = 4^2.
a(2) = 5 since 5>2 and 25 = 5^2.

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) (10 x + 1) - 1] + 1)^2, 10^(d + 1)]]]; Array[f, 65] (* Robert G. Wilson v, Nov 23 2015, after the algorithm of David W. Wilson in A090566 *)
lnk[n_]:=Module[{k=n+1}, While[!IntegerQ[Sqrt[n 10^IntegerLength[k]+k]], k++]; k]; Array[lnk, 70, 0] (* Harvey P. Dale, Sep 01 2023 *)

Prog

(PARI) a(n)=s=Str(n); k=n+1; while(!issquare(eval(concat(s, Str(k)))), k++); return(k)
vector(100, n, a(n))
(PARI) A048761 = t->(sqrtint(t-1)+1)^2
A243091(n)={my(d=#Str(n), a=A048761((1+10^d)*n)); a>=(n+1)*10^d && a=A048761((n*10+1)*10^d); a%10^(d+(a>=100^d))} \\ M. F. Hasler, Nov 24 2015

Crossrefs

Cf. A090566.

Sequence in context: A243093 A101634 A071176 * A195786 A201330 A089826

Adjacent sequences: A243088 A243089 A243090 * A243092 A243093 A243094

Keyword

nonn,base

Author

Derek Orr, Aug 18 2014

Extensions

a(0)=1 added by N. J. A. Sloane, Nov 24 2015

Status

approved