A089717 Triangular numbers with palindromic indices.

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 5151, 6216, 7381, 8646, 10011, 11476, 13041, 14706, 16471, 18336, 20503, 22578, 24753, 27028, 29403, 31878, 34453, 37128, 39903, 42778, 46056, 49141, 52326, 55611

Offset: 1

Author

Giovanni Teofilatto, Nov 24 2004

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008509, A000217, A002113.

Programs

Mathematica

Module[{nn=500,paldx},paldx=Table[If[PalindromeQ[n],1,0],{n,0,nn}];Pick[Accumulate[ Range[ 0,nn]],paldx,1]] (* Harvey P. Dale, Jun 11 2024 *)

Python

from itertools import chain, count, islice
def A089717_gen(): # generator of terms
    return map(lambda n:n*(n+1)//2,chain((0,),chain.from_iterable(chain((int((s:=str(d))+s[-2::-1]) for d in range(10**l,10**(l+1))), (int((s:=str(d))+s[::-1]) for d in range(10**l,10**(l+1)))) for l in count(0))))
A089717_list = list(islice(A089717_gen(),20)) # Chai Wah Wu, Jun 23 2022

Formula

a(n) = A000217(A002113(n)).

Extensions

Definition corrected by Lambert.Klasen and David Wasserman, Oct 04 2005

More terms from David Wasserman and Klaus Brockhaus, Oct 04 2005