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%I #93 Jul 25 2020 21:25:49
%S 3,5,10,21,36,60,80,120,180,264,252,360,300,960,900,720,1080,1440,
%T 1800,1680,2160,2880,5616,3780,2520,3600,6120,6720,6300,5040,11340,
%U 7560,14112,10800,9240,10080,13860,12600,31200,15120,22680,20160,18480,39312,33264,39600,25200,30240
%N Smallest number that is palindromic (with at least 2 digits) in n bases.
%C Smallest number k that is palindromic in n bases b, 1 < b < k.
%C Only a(1), a(2), a(3), a(4) & a(7) are not congruent to 0 (mod 12). - _Robert G. Wilson v_, Oct 21 2014
%C First occurrence of k beginning with 0 in A135551. - _Robert G. Wilson v_, Jun 30 2017
%H Robert G. Wilson v, <a href="/A037183/b037183.txt">Table of n, a(n) for n = 1..342</a> (first 100 terms from Giovanni Resta)
%H Robert G. Wilson v, <a href="/A037183/a037183.txt">Smallest number which is palindromic in n bases or 0 if no such number is known</a>
%e 3 = 11 in base 2.
%e 5 = 101 in base 2 and 11 in base 4.
%e 10 is a palindrome in bases 3, 4 and 9: 101(3), 22(4) and 11(9). So a(3)=10.
%t f[n_] := Module[{idn, s = Floor@ Sqrt[n + 1] - 1}, lng = Table[ If[ Reverse[ idn = IntegerDigits[n, b]] == idn, {b}, Sequence @@ {}], {b, 2, s + 1}]; If[ IntegerQ@ Sqrt[n + 1], -1, 0] + Length@ lng + Count[ Mod[n, Range@ s], 0]]; f[n_] := 0 /; n < 3; t = Table[0, {700}]; k = 3; While[k < 1100000001, a = f[k]; If[ t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; Take[t, 310] (* _Robert G. Wilson v_, Nov 02 2014 *)
%Y Cf. A065531, A107129, A135549.
%K nonn,base,nice
%O 1,1
%A _Erich Friedman_, Dec 11 1999
%E More terms from _David W. Wilson_
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