cp's OEIS Frontend

A068149 Triangular numbers in which neighboring digits differ at most by 1. Allowed neighbors of 9 are 0, 8 and 9.

%I A068149 #24 Sep 23 2024 11:32:22
%S A068149 0,1,3,6,10,21,45,55,66,78,210,666,990,2211,3321,5565,6555,8778,10011,
%T A068149 90100,112101,222111,232221,443211,887778,5433456,5456556,5656566,
%U A068149 5676765,22221111,22321221,34565455,88877778,211099878,212210901
%N A068149 Triangular numbers in which neighboring digits differ at most by 1. Allowed neighbors of 9 are 0, 8 and 9.
%C A068149 Includes (2 * 10^(2*k) - 10^k - 1)/9 and (8 * 10^(2*k) - 10^(k+1) + 2)/9 for k >= 1, and (2 * 10^(2*k) + 89 * 10^k + 989)/9 for k >= 2. - _Robert Israel_, Sep 22 2024
%H A068149 Robert Israel, <a href="/A068149/b068149.txt">Table of n, a(n) for n = 1..95</a> (n = 1 .. 65 from Andrew Howroyd)
%p A068149 f:= proc(n) local i;
%p A068149    seq(10*n+i, i= sort([n-1, n, n+1] mod 10))
%p A068149 end proc:
%p A068149 istri:= proc(n) issqr(1+8*n) end proc:
%p A068149 S:= [$1..9]: R:= 0,1,3,6: count:= 4:
%p A068149 for i from 1 while count < 95 do
%p A068149   for k from i to i+1 do
%p A068149     for s in S do
%p A068149       tmin:= ceil(sqrt(8*s*10^k+1));
%p A068149       if tmin::even then tmin:= tmin+1 fi;
%p A068149       for t from tmin to floor(sqrt(8*(s+1)*10^k-7)) by 2 do
%p A068149         x:= (t-1)/2; y:= x*(x+1)/2;
%p A068149         L:= convert(y,base,10);
%p A068149         if convert(L[2..-1]-L[1..-2] mod 10, set) subset {0,1,9} then
%p A068149           R:= R,y; count:= count+1;
%p A068149   fi od od od;
%p A068149   if count < 95 then S:= map(f, S) fi;
%p A068149 od:
%p A068149 R; # _Robert Israel_, Sep 23 2024
%t A068149 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 A068149 Select[Accumulate[Range[0,30000]],Max[Select[Abs[Differences[ IntegerDigits[ #]]], #!=9&]]<2&] (* _Harvey P. Dale_, Oct 09 2013 *)
%Y A068149 Intersection of A000217 and A376425.
%K A068149 base,easy,nonn
%O A068149 1,3
%A A068149 _Amarnath Murthy_, Feb 23 2002
%E A068149 Edited and extended by _Robert G. Wilson v_ and _Sascha Kurz_, Mar 01 2002
%E A068149 Offset changed by _Andrew Howroyd_, Sep 22 2024