A162703 Palindromes in A005448.

1, 4, 15151, 45154, 66466, 92629, 98689, 4976794, 6424246, 648616846, 136287949782631, 479573060375974, 69465717171756496, 4345218593958125434, 42097537753535773579024, 58071646151315164617085, 6220959179720279719590226, 458122911526080625119221854

Offset

1,2

Comments

Essentially the palindromes which are sums of three consecutive triangular numbers T.

Indices of the centered triangular numbers: 1, 2, 101, 174, 211, 249, 257, 1822, 2070, 20795, 9531980, 17880587, 215198695, ..., (A195903). - Robert G. Wilson v

a(18) > 10^25. - Donovan Johnson, Sep 29 2011

a(31) > 10^40. - Patrick De Geest, May 23 2021

Links

Patrick De Geest, Table of n, a(n) for n = 1..30

Patrick De Geest, Palindromic Centered Polygonal Numbers

Terry Trotter, Polygonal Numbers from the Wayback machine

Formula

a(n) = (3*m^2 - 3*m + 2)/2 or a(n) = (3*n^2 + 3*n + 2)/2 with n = m - 1.

Example

T(99) + T(100) + T(101) = 15151.
T(172) + T(173) + T(174) = 45154.

Mathematica

n = 1; lst = {}; While[n < 10^10, ctn = 3 n (n - 1)/2 + 1; id = IntegerDigits@ ctn; If[id == Reverse@id, AppendTo[lst, ctn]; Print[{n, ctn}]]; n++ ]; lst (* Robert G. Wilson v *)

Crossrefs

Cf. A000217, A005448, A195903.

Sequence in context: A134368 A152840 A003832 * A258101 A265215 A070157

Adjacent sequences: A162700 A162701 A162702 * A162704 A162705 A162706

Keyword

nonn,base

Author

Claudio Meller, Jul 11 2009

Extensions

Edited and extended by R. J. Mathar and Robert G. Wilson v, Jul 13 2009

a(14)-a(17) from Donovan Johnson, Sep 29 2011

a(18)-a(30) from Patrick De Geest, May 23 2021

Status

approved