A100844 Smallest m greater than n such that m^2 contains n^2 in its decimal representation.

10, 4, 7, 7, 13, 15, 19, 43, 42, 41, 90, 110, 38, 130, 140, 35, 160, 170, 57, 190, 80, 210, 220, 227, 240, 75, 260, 223, 279, 196, 70, 219, 320, 330, 340, 285, 360, 370, 380, 390, 400, 410, 343, 136, 440, 205, 460, 470, 480, 490, 150, 510, 520, 530, 540, 305, 481

Offset

0,1

Comments

a(n) <= 10*n; a(A102576(n)) < 10*A102576(n), a(A102577(n)) = 10*A102577(n). - Reinhard Zumkeller, Jan 15 2005

Links

Zak Seidov, Table of n, a(n) for n = 0..1000

Example

n=3: (3+1)^2 = 16, (3+2)^2 = 25 and (3+3)^2 = 36 do not contain 9 = 3^2, but 7^2 = 49 contains 9, therefore a(3) = 7.

Mathematica

p = -1; s = {}; m = 100; Do[p = p + 1; idp = IntegerDigits[p^2]; le = Length[idp]; q = p; Label[1]; q = q + 1; par = Partition[IntegerDigits[q^2], le, 1]; If[MemberQ[par, idp], AppendTo[s, q]; Goto[2], Goto[1]]; Label[2], {m}]; s (* Zak Seidov, Dec 19 2014 *)
f[n_] := Block[{sidn = ToString[n^2], k = n + 1}, While[ StringPosition[ ToString[k^2], sidn] == {}, k++]; k]; Array[f, 60, 0] (* Robert G. Wilson v, Dec 19 2014 *)

Prog

(Python)
def a(n):
    s, m = str(n*n), n+1
    while s not in str(m*m): m += 1
    return m
print([a(n) for n in range(57)]) # Michael S. Branicky, Oct 04 2021

Crossrefs

Cf. A000290, A064735, A102576, A102577.

Sequence in context: A153690 A018811 A309707 * A076587 A266999 A166204

Adjacent sequences: A100841 A100842 A100843 * A100845 A100846 A100847

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 14 2005

Status

approved