%I #26 May 24 2021 00:31:50
%S 1,4,15151,45154,66466,92629,98689,4976794,6424246,648616846,
%T 136287949782631,479573060375974,69465717171756496,
%U 4345218593958125434,42097537753535773579024,58071646151315164617085,6220959179720279719590226,458122911526080625119221854
%N Palindromes in A005448.
%C Essentially the palindromes which are sums of three consecutive triangular numbers T.
%C Indices of the centered triangular numbers: 1, 2, 101, 174, 211, 249, 257, 1822, 2070, 20795, 9531980, 17880587, 215198695, ..., (A195903). - _Robert G. Wilson v_
%C a(18) > 10^25. - _Donovan Johnson_, Sep 29 2011
%C a(31) > 10^40. - _Patrick De Geest_, May 23 2021
%H Patrick De Geest, <a href="/A162703/b162703.txt">Table of n, a(n) for n = 1..30</a>
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/centered.htm">Palindromic Centered Polygonal Numbers</a>
%H Terry Trotter, <a href="https://web.archive.org/web/20160420101547/http://trottermath.net/polygonal-numbers/">Polygonal Numbers</a> from the Wayback machine
%F a(n) = (3*m^2 - 3*m + 2)/2 or a(n) = (3*n^2 + 3*n + 2)/2 with n = m - 1.
%e T(99) + T(100) + T(101) = 15151.
%e T(172) + T(173) + T(174) = 45154.
%t 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_ *)
%Y Cf. A000217, A005448, A195903.
%K nonn,base
%O 1,2
%A _Claudio Meller_, Jul 11 2009
%E Edited and extended by _R. J. Mathar_ and _Robert G. Wilson v_, Jul 13 2009
%E a(14)-a(17) from _Donovan Johnson_, Sep 29 2011
%E a(18)-a(30) from _Patrick De Geest_, May 23 2021
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