A281822 Least number k such that (k+n)^2 contains k as a substring.

1, 8, 6, 1, 4, 9, 62, 6, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4, 1, 5, 1, 2, 9, 2, 4, 2, 92, 9, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 3, 1, 3, 3, 1, 2, 1, 4, 4, 2, 4, 4, 2, 4, 1, 5, 1, 1, 5, 2, 4, 2, 4, 2, 1, 5, 1, 6, 5, 2, 4, 8, 6

Offset: 0

Author

Paolo P. Lava, Jan 31 2017

Keywords

• nonn
• base
• easy

Examples

			a(1) = 8 because (8 + 1)^2 = 9^2 = 81 contains 8 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, A281823.

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);

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.