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%I #7 Mar 19 2017 19:29:56
%S 1,2,3,11,26,111,1111,11111,105462,111111,460688,753576,1111111,
%T 2806538,3513626,5858612,11111111,23335688,111111111,674874474,
%U 8226042716,2131535935501,81655720279388
%N Numbers k, not ending in 0, such that the consecutive digits of k^2 differ by 0 or 1.
%C Equivalently, numbers not ending in 0, whose square belong to A032981.
%C All members k ending in 1 are generators of infinite numbers of the form k*10^e which satisfy the same property. In a sense, here we list only "primitive" terms, not ending in 0.
%C a(24) > 10^17, if it exists.
%e 81655720279388 belongs to this sequence because the consecutive digits of its square, 6667656654345656676777654544, differ by 0 or 1.
%t Select[Range[10^6], Mod[#, 10] > 0 && Max@ Abs@ Differences@ IntegerDigits[ #^2] <= 1 &]
%Y Cf. A032981, A048412, A079036.
%K nonn,base,more
%O 1,2
%A _Giovanni Resta_, Mar 19 2017