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Numbers k such that the decimal expansion of k^2 contains no pair of consecutive equal digits.
4

%I #20 Oct 16 2019 01:33:02

%S 0,1,2,3,4,5,6,7,8,9,11,13,14,16,17,18,19,22,23,24,25,26,27,28,29,31,

%T 32,33,36,37,39,41,42,43,44,45,48,49,51,52,53,54,55,56,57,59,61,63,64,

%U 66,68,69,71,72,73,74,75,77,78,79,81,82,84,86,87,89,91,92,93,95,96,97

%N Numbers k such that the decimal expansion of k^2 contains no pair of consecutive equal digits.

%H Zak Seidov and Michael De Vlieger, <a href="/A050741/b050741.txt">Table of n, a(n) for n = 1..10471</a>, a(n) < 25,000 (First 1057 terms from Zak Seidov)

%e 10 is absent because 10^2=100 with repeating 0,

%e 12 is absent because 12^2=144 with repeating 4,

%e 21 is absent because 21^2=441 with repeating 4.

%t Select[Range[0,97],FreeQ[Differences[IntegerDigits[#^2]],0]&] (* _Jayanta Basu_, May 31 2013 *)

%Y Cf. A043096, A050749, A135463, A134962.

%K nonn,base

%O 1,3

%A _Patrick De Geest_, Sep 15 1999

%E Edited by _N. J. A. Sloane_, Mar 16 2008