A162703 Palindromes in A005448.

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

Offset: 1

Author

Claudio Meller, Jul 11 2009

Keywords

• nonn
• base

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

Examples

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

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

Crossrefs

Cf. A000217, A005448, A195903.

Programs

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 *)

Formula

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

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