A061455 Triangular numbers whose digit reversal is also a triangular number.

0, 1, 3, 6, 10, 55, 66, 120, 153, 171, 190, 300, 351, 595, 630, 666, 820, 3003, 5995, 8778, 15051, 17578, 66066, 87571, 156520, 180300, 185745, 547581, 557040, 617716, 678030, 828828, 1269621, 1461195, 1680861, 1851850, 3544453, 5073705, 5676765, 5911641

Offset: 1

Author

Amarnath Murthy, May 03 2001

Keywords

• nonn
• base
• easy

Examples

			153 is in the sequence because (1) it is a triangular number and (2) its reversal 351 is also a triangular number.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..162 (terms < 10^18)

Crossrefs

Cf. A000217, A003098, A004086, A066528, A066569, A069673.

Programs

Maple

read("transforms");
isA000217 := proc(n) issqr(1+8*n) ;end proc:
isA061455 := proc(n) isA000217(n) and isA000217(digrev(n)) ; end proc:
for n from 0 to 60000 do T := A000217(n) ; if isA061455(T) then printf("%d,", T) ; end if; end do: # R. J. Mathar, Dec 13 2010

Mathematica

TriangularNumberQ[k_] := If[IntegerQ[1/2 (Sqrt[1 + 8 k] - 1)], True, False]; Select[Range[0, 5676765], TriangularNumberQ[#] && TriangularNumberQ[FromDigits[Reverse[IntegerDigits[#]]]] &] (* Ant King, Dec 13 2010 *)

PARI

isok(n) = ispolygonal(n, 3) && ispolygonal(fromdigits(Vecrev(digits(n))), 3); \\ Michel Marcus, Apr 14 2019

Formula

a(n)=A000217(k) and A004086(a(n))=A000217(j) for some k and j. - R. J. Mathar, Jun 02 2006

Extensions

More terms from Erich Friedman, May 08 2001

Edited by N. J. A. Sloane, Aug 13 2008 at the suggestion of R. J. Mathar