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.

3, 4, 25, 6, 14, 32, 54, 30, 11, 84, 39, 140, 75, 176, 102, 198, 19, 220, 147, 110, 69, 384, 175, 416, 486, 420, 58, 570, 279, 544, 429, 306, 245, 684, 296, 380, 663, 880, 615, 1134, 258, 1012, 1035, 1104, 47, 1392, 539, 1500, 1071, 1508, 53, 2106

Offset: 2

Author

Naohiro Nomoto, Dec 06 2001

Keywords

• easy
• base
• nonn

Comments

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

Examples

			From _Robert G. Wilson v_, Dec 22 2021: (Start)
a(2) = 3 since A016026(3) = 2;
a(3) = 4 since A016026(4) = 3;
a(4) = 25 since A016026(25) = 4; etc. (End)
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 2..10000 (first 441 terms from Robert Israel).

Crossrefs

Cf. A016026, A065531, A249634.

Programs

Maple

N:= 100:
f:= proc(m) local k,L;
   for k from 2 to m do
     L:= convert(m,base,k);
     if L = ListTools:-Reverse(L) then return k fi
   od;
   FAIL
end proc:
V:= Array(2..N):
count:= 0:
for m from 3 while count < N-1 do
  v:= f(m);
  if v = FAIL or v > N then next fi;
  if V[v] = 0 then count:= count+1; V[v]:= m;
  fi
od:
convert(V,list); # Robert Israel, Apr 08 2019

Mathematica

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 *)

Extensions

Definition edited by N. J. A. Sloane, Apr 08 2019