|
%I #25 May 21 2022 19:41:16
%S 0,1,3,6,10,55,66,120,153,171,190,300,351,595,630,666,820,3003,5995,
%T 8778,15051,17578,66066,87571,156520,180300,185745,547581,557040,
%U 617716,678030,828828,1269621,1461195,1680861,1851850,3544453,5073705,5676765,5911641
%N Triangular numbers whose digit reversal is also a triangular number.
%H Jon E. Schoenfield, <a href="/A061455/b061455.txt">Table of n, a(n) for n = 1..162</a> (terms < 10^18)
%F a(n)=A000217(k) and A004086(a(n))=A000217(j) for some k and j. - _R. J. Mathar_, Jun 02 2006
%e 153 is in the sequence because (1) it is a triangular number and (2) its reversal 351 is also a triangular number.
%p read("transforms");
%p isA000217 := proc(n) issqr(1+8*n) ;end proc:
%p isA061455 := proc(n) isA000217(n) and isA000217(digrev(n)) ; end proc:
%p 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
%t 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 *)
%o (PARI) isok(n) = ispolygonal(n, 3) && ispolygonal(fromdigits(Vecrev(digits(n))), 3); \\ _Michel Marcus_, Apr 14 2019
%Y Cf. A000217, A003098, A004086, A066528, A066569, A069673.
%K nonn,base,easy
%O 1,3
%A _Amarnath Murthy_, May 03 2001
%E More terms from _Erich Friedman_, May 08 2001
%E Edited by _N. J. A. Sloane_, Aug 13 2008 at the suggestion of _R. J. Mathar_
|
