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
Examples
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.
Links
- Zak Seidov, Table of n, a(n) for n = 0..1000
Programs
-
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 *) -
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
Comments