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

1,3

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..95 (n = 1 .. 65 from Andrew Howroyd)

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 *)

Crossrefs

Intersection of A000217 and A376425.

Sequence in context: A027671 A167617 A274018 * A068709 A068804 A117834

Adjacent sequences: A068146 A068147 A068148 * A068150 A068151 A068152

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 23 2002

Extensions

Edited and extended by Robert G. Wilson v and Sascha Kurz, Mar 01 2002

Offset changed by Andrew Howroyd, Sep 22 2024

Status

approved