%I #8 Dec 05 2013 19:55:11
%S 0,1,3,6,10,21,45,55,66,78,210,666,990,2211,3321,5565,6555,8778,10011,
%T 90100,112101,222111,232221,443211,887778,5433456,5456556,5656566,
%U 5676765,22221111,22321221,34565455,88877778,211099878,212210901
%N Triangular numbers in which neighboring digits differ at most by 1. Allowed neighbors of 9 are 0, 8 and 9.
%t Do[a = IntegerDigits[n(n + 1)/2]; k = 1; l = Length[a]; While[k < l && (Abs[a[[k]]- a[[k + 1]]] < 2 || Abs[a[[k]] - a[[k + 1]]] > 8), k++ ]; If[k == l, Print[n(n + 1)/2]], {n, 0, 10^5} ]
%t Select[Accumulate[Range[0,30000]],Max[Select[Abs[Differences[ IntegerDigits[ #]]], #!=9&]]<2&] (* _Harvey P. Dale_, Oct 09 2013 *)
%Y Cf. A000217.
%K base,easy,nonn
%O 0,3
%A _Amarnath Murthy_, Feb 23 2002
%E Edited and extended by _Robert G. Wilson v_ and _Sascha Kurz_, Mar 01 2002
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