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

1,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A008509, A000217, A002113.

Sequence in context: A046489 A277209 A361751 * A050760 A075057 A069792

Adjacent sequences: A089714 A089715 A089716 * A089718 A089719 A089720

Keyword

nonn,base

Author

Giovanni Teofilatto, Nov 24 2004

Extensions

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

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

Status

approved