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A065809 a(n) is the smallest number m > n such that m is palindromic in base n and is not palindromic in bases b with 2 <= b < n.

%I A065809 #28 Jan 27 2022 21:20:59
%S A065809 3,4,25,6,14,32,54,30,11,84,39,140,75,176,102,198,19,220,147,110,69,
%T A065809 384,175,416,486,420,58,570,279,544,429,306,245,684,296,380,663,880,
%U A065809 615,1134,258,1012,1035,1104,47,1392,539,1500,1071,1508,53,2106
%N A065809 a(n) is the smallest number m > n such that m is palindromic in base n and is not palindromic in bases b with 2 <= b < n.
%C A065809 Index at which first occurrence of n occurs in A016026 when the palindrome is multidigit. Only the first two terms of A016026 are single-digit palindromes. - _Robert G. Wilson v_, Dec 22 2021
%H A065809 Robert G. Wilson v, <a href="/A065809/b065809.txt">Table of n, a(n) for n = 2..10000</a> (first 441 terms from Robert Israel).
%e A065809 From _Robert G. Wilson v_, Dec 22 2021: (Start)
%e A065809 a(2) = 3 since A016026(3) = 2;
%e A065809 a(3) = 4 since A016026(4) = 3;
%e A065809 a(4) = 25 since A016026(25) = 4; etc. (End)
%p A065809 N:= 100:
%p A065809 f:= proc(m) local k,L;
%p A065809    for k from 2 to m do
%p A065809      L:= convert(m,base,k);
%p A065809      if L = ListTools:-Reverse(L) then return k fi
%p A065809    od;
%p A065809    FAIL
%p A065809 end proc:
%p A065809 V:= Array(2..N):
%p A065809 count:= 0:
%p A065809 for m from 3 while count < N-1 do
%p A065809   v:= f(m);
%p A065809   if v = FAIL or v > N then next fi;
%p A065809   if V[v] = 0 then count:= count+1; V[v]:= m;
%p A065809   fi
%p A065809 od:
%p A065809 convert(V,list); # _Robert Israel_, Apr 08 2019
%t A065809 fpb = Compile[{{n, _Integer}}, Module[{b = 2, idn}, While[ Reverse[idn = IntegerDigits[n, b]] != idn, b++]; b]]; k = 3; t[_] := 0; While[k < 2200, a = fpb@ k; If[ t[a] == 0, t[a] = k]; k++]; t@# & /@ Range[2, 53] (* _Robert G. Wilson v_, Dec 22 2021 *)
%Y A065809 Cf. A016026, A065531, A249634.
%K A065809 easy,base,nonn
%O A065809 2,1
%A A065809 _Naohiro Nomoto_, Dec 06 2001
%E A065809 Definition edited by _N. J. A. Sloane_, Apr 08 2019