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%I #36 Oct 26 2015 13:12:56
%S 1,3,5,10,21,36,60,80,120,180,252,300,720,1080,1440,1680,2160,2520,
%T 3600,5040,7560,9240,10080,12600,15120,18480,25200,27720,36960,41580,
%U 45360,50400,55440,83160,110880,131040,166320,221760,277200,332640,360360
%N Numbers n which are palindromic in more bases b, 1<b<n, than any previous number.
%C Records by number in A037183, by indices in A065531.
%C Except for 3, 5 and 21 they are all even and except for the first seven, they are all multiples of twelve.
%D Michael Trott, The Mathematica GuideBook for Programming, Springer, 2004, page 218.
%H Robert G. Wilson v, <a href="/A107129/b107129.txt">Table of n, a(n) for n = 0..91</a>
%e 1 has no palindromic representation in bases 2 to n.
%e 3 = 11_2.
%e 5 = 101_2, 11_4.
%e 10 = 101_3, 22_4, 11_9.
%e 21 = 10101_2, 111_4, 33_6, 11_20.
%e 36960 = 5775_19, 3(90)3_97, (176)(176)_209, (168)(168)_219,
%e (165)(165)_223, (160)(160)_230, (154)(154)_239, (140)(140)_263, (132)(132)_279,
%e (120)(120)_307, (112)(112)_329, (110)(110)_335, (105)(105)_351, (96)(96)_384,
%e (88)(88)_419, (84)(84)_439, (80)(80)_461, (77)(77)_479, (70)(70)_527,
%e (66)(66)_559, (60)(60)_615, (56)(56)_659, (55)(55)_671, (48)(48)_769,
%e (44)(44)_839, (42)(42)_879, (40)(40)_923, (35)(35)_1055, (33)(33)_1119,
%e (32)(32)_1154, (30)(30)_1231, (28)(28)_1319, (24)(24)_1539, (22)(22)_1679,
%e (21)(21)_1759, (20)(20)_1847, (16)(16)_2309, (15)(15)_2463, (14)(14)_2639,
%e (12)(12)_3079, (11)(11)_3359, (10)(10)_3695, 88_4619, 77_5279, 66_6159, 55_7391,
%e 44_9239, 33_12319, 22_18479, 11_36959.
%t f[n_] := Block[{s = Floor@ Sqrt[n + 1] - 1, b = 2, c = If[IntegerQ@ Sqrt[n + 1], -2, -1]}, While[b < s + 2, idn = IntegerDigits[n, b]; If[ idn == Reverse@ idn, c++]; b++]; c + Count[ Mod[n, Range@ s], 0]]; f[n_] := 0 /; n < 3;
%t k = 0; mx = -1; lst = {}; While[ k < 360000001, c = f@ k; If[ c > mx, AppendTo[lst, k]; mx = c]; k++]; lst
%Y Cf. A037183, A065531, A106801, A135549.
%K nonn,base
%O 0,2
%A Michael Trott (mtrott(AT)wolfram.com) and _Robert G. Wilson v_, May 12 2005
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