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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A081975 A160965 A069708 * A068071 A067269 A352057

Adjacent sequences: A061452 A061453 A061454 * A061456 A061457 A061458

Keyword

nonn,base,easy

Author

Amarnath Murthy, May 03 2001

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

Status

approved