A281823 Least number k such that (k-n)^2 contains k as a substring.

1, 12, 1, 16, 108, 1, 4, 2, 116, 3, 1, 1, 1, 1, 1, 1, 4, 2, 2, 2, 1, 3, 1, 9, 4, 2, 4, 2, 5, 2, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 3, 2, 1, 3, 1, 2, 3, 3, 3, 2, 4, 3, 1, 4, 1, 1, 4, 2, 3, 2, 4, 2, 1, 2, 1, 4, 2, 6

Offset: 0

Author

Paolo P. Lava, Jan 31 2017

Keywords

• nonn
• base
• easy

Examples

			a(1) = 12 because (12 - 1)^2 = 11^2 = 121 contains 12 as a substring and it is the least number with this property.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A018834, A281822.

Programs

Maple

with(numtheory): P:= proc(q) local a,b,d,j,k,n,ok;
for n from 0 to q do for k from 1 to q do a:=ilog10(k)+1; b:=(n-k)^2; d:=ilog10((k-n)^2)-ilog10(k)+1;
ok:=0; for j from 1 to d do if k=(b mod 10^a) then ok:=1; break; else b:=trunc(b/10); fi; od;
if ok=1 then print(k); break; fi; od; od; end: P(10^6);

Mathematica

nk[n_]:=Module[{k=1},While[SequenceCount[IntegerDigits[(k-n)^2],IntegerDigits[ k]]==0,k++];k]; Array[lnk,90,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 13 2021 *)

Extensions

Typo in definition corrected by Harvey P. Dale, Feb 27 2017.

Entries, Maple code and b-file corrected at the suggestion of Harvey P. Dale, Feb 28 2017.