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A061455
Triangular numbers whose digit reversal is also a triangular number.
7
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
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