A052081 Numbers k such that k^2 is a square whose decimal expansion's digits are grouped together.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 78, 79, 80, 82, 83

Offset: 1

Author

Patrick De Geest, Jan 15 2000

Keywords

• nonn
• base

Examples

			81 is not a term since in 81^2 = 6561, the two 6's are separated by the 5.
88 is a term since in 88^2 = 7744, the 7 and 4 are grouped.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052082, A052085, A052086, A052083, A052084.

Programs

Maple

filter:= proc(n) local L,i,v,V;
  L:= convert(n^2,base,10);
  for i from 1 to nops(L) do
    v:= L[i];
    if not assigned(V[v]) then V[v]:= i
    elif V[v] < i-1 then return false
    else V[v]:= i
    fi
  od;
  true
end proc:
select(filter, [$0..100]); # Robert Israel, Nov 08 2023