A069702 Triangular numbers with internal digits also forming a triangular number.

105, 136, 210, 231, 300, 406, 435, 465, 561, 630, 666, 703, 861, 903, 1035, 2016, 2211, 2556, 3003, 3916, 4005, 5151, 6105, 6216, 6555, 6786, 8001, 8911, 9453, 10011, 10153, 19900, 20100, 20910, 23005, 28203, 39903, 41905, 46665, 48205

Offset

1,1

Comments

Includes (2*10^(2*k)-10^k-1)/9 for every k, so the sequence is infinite. - Robert Israel, Aug 28 2018

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 210 terms from Robert Israel)

Example

3916 is a member as 3916 and 91 both are triangular.

Maple

filter:= proc(x) local t, m;
  t:= floor(x/10);
  m:= ilog10(t);
  t:= t - floor(t/10^m)*10^m;
  issqr(8*t+1)
end proc:
select(filter, [seq(x*(x+1)/2, x=14..1000)]); # Robert Israel, Aug 28 2018

Mathematica

s=Select[Range[14, 400], IntegerQ[Sqrt[1+8FromDigits[Drop[Drop[IntegerDigits[ #(#+1)/2], 1], -1]]]]&]; s(s+1)/2

Crossrefs

Cf. A077366.

Sequence in context: A267891 A097217 A115935 * A239589 A203614 A252069

Adjacent sequences: A069699 A069700 A069701 * A069703 A069704 A069705

Keyword

base,nonn

Author

Amarnath Murthy, Apr 06 2002

Extensions

Edited by Dean Hickerson, Apr 09 2002

Edited by Robert Israel, Aug 28 2018

Status

approved