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Numbers n such that base 10 representation of n does not contain a block of digits which is a square: blocks like 0, 1, 4, 9, 36, 121, ... are forbidden.
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%I #10 Mar 05 2014 17:34:21

%S 2,3,5,6,7,8,22,23,26,27,28,32,33,35,37,38,52,53,55,56,57,58,62,63,65,

%T 66,67,68,72,73,75,76,77,78,82,83,85,86,87,88,222,223,226,227,228,232,

%U 233,235,237,238,262,263,265,266,267,268,272,273,275,276,277,278,282

%N Numbers n such that base 10 representation of n does not contain a block of digits which is a square: blocks like 0, 1, 4, 9, 36, 121, ... are forbidden.

%C "Squarefree" integers. The usual definition of "squarefree" means that there is no square as divisor, but here we consider numbers without any square in their decimal expansion. Of the first 1000 integers only 232 are in the sequence, while 608 are squarefree in the usual sense. - _Zak Seidov_, Sep 26 2002

%C Sequence is infinite, since numbers consisting of only the digits 2, 3, 7, and 8 cannot contain squares. In particular this shows a(n) << n^1.661. - _Charles R Greathouse IV_, Mar 05 2014

%e a(7) = 22 because both 2 and 22 are nonsquares.

%e 323 and 326 are members because they have no squares 0, 1, 4, 9, 16, 25, 36... in their decimal expansion; while the two numbers between, 324 and 325, are not members because 324 contains square 4 and 325 - square 25.

%Y A subsequence of A000037.

%K nonn,base

%O 1,1

%A Noam Katz (noamkj(AT)hotmail.com), Jan 25 2001