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

1,3

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A043096 A355301 A010784 * A031995 A023752 A048737

Adjacent sequences: A052078 A052079 A052080 * A052082 A052083 A052084

Keyword

nonn,base

Author

Patrick De Geest, Jan 15 2000

Status

approved