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A052081
Numbers k such that k^2 is a square whose decimal expansion's digits are grouped together.
6
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
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
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Jan 15 2000
STATUS
approved