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A162703 Palindromes in A005448. 2

%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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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)