A068149 Triangular numbers in which neighboring digits differ at most by 1. Allowed neighbors of 9 are 0, 8 and 9.
0, 1, 3, 6, 10, 21, 45, 55, 66, 78, 210, 666, 990, 2211, 3321, 5565, 6555, 8778, 10011, 90100, 112101, 222111, 232221, 443211, 887778, 5433456, 5456556, 5656566, 5676765, 22221111, 22321221, 34565455, 88877778, 211099878, 212210901
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..95 (n = 1 .. 65 from Andrew Howroyd)
Programs
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Maple
f:= proc(n) local i; seq(10*n+i, i= sort([n-1, n, n+1] mod 10)) end proc: istri:= proc(n) issqr(1+8*n) end proc: S:= [$1..9]: R:= 0,1,3,6: count:= 4: for i from 1 while count < 95 do for k from i to i+1 do for s in S do tmin:= ceil(sqrt(8*s*10^k+1)); if tmin::even then tmin:= tmin+1 fi; for t from tmin to floor(sqrt(8*(s+1)*10^k-7)) by 2 do x:= (t-1)/2; y:= x*(x+1)/2; L:= convert(y,base,10); if convert(L[2..-1]-L[1..-2] mod 10, set) subset {0,1,9} then R:= R,y; count:= count+1; fi od od od; if count < 95 then S:= map(f, S) fi; od: R; # Robert Israel, Sep 23 2024 -
Mathematica
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} ] Select[Accumulate[Range[0,30000]],Max[Select[Abs[Differences[ IntegerDigits[ #]]], #!=9&]]<2&] (* Harvey P. Dale, Oct 09 2013 *)
Extensions
Edited and extended by Robert G. Wilson v and Sascha Kurz, Mar 01 2002
Offset changed by Andrew Howroyd, Sep 22 2024
Comments