A337164 a(n) is the least base, other than 10, in which the decimal digits of n represent a prime, or 0 if there is no such base.

3, 4, 0, 6, 0, 8, 0, 0, 0, 2, 3, 4, 7, 6, 7, 12, 9, 14, 0, 3, 0, 4, 0, 6, 0, 8, 0, 11, 0, 4, 5, 0, 5, 6, 0, 8, 11, 0, 0, 7, 0, 5, 0, 6, 0, 9, 0, 11, 0, 6, 7, 8, 11, 0, 7, 8, 9, 14, 0, 7, 0, 0, 0, 7, 0, 9, 0, 0, 0, 16, 11, 8, 9, 8, 11, 0, 9, 14, 0, 9, 0, 13, 0, 12, 0, 9, 0, 11, 0, 12, 11, 0, 11

Offset

2,1

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Example

a(12) = 3 because 12_3 = 5 is prime.

Maple

f:= proc(n) local L, b, i, x, v, p;
  L:= convert(n, base, 10);
  if L[1] = 0 or igcd(op(L)) > 1 or not irreduc(add(L[i]*x^(i-1), i=1..nops(L))) then return 0 fi;
  b:= max(L)+1;
  if b = 10 then b:= 11 fi;
  v:= add(L[i]*b^(i-1), i=1..nops(L));
  if isprime(v) then return b fi;
  for p in numtheory:-factorset(v) do
    if andmap(t -> add(L[i]*t^(i-1), i=1..nops(L)) mod p = 0, [$0..p-1]) then return 0 fi;
  od;
  for b from b+1 to 10^4 do
    if b = 10 then next fi;
    if isprime(add(L[i]*b^(i-1), i=1..nops(L))) then return b fi
  od;
  FAIL
end proc:
f(2):= 3: f(3):= 4: f(5):= 6: f(7):= 8:
map(f, [$2..200]);

Crossrefs

Sequence in context: A086230 A197485 A158677 * A105576 A105826 A110665

Adjacent sequences: A337161 A337162 A337163 * A337165 A337166 A337167

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Jan 28 2021

Status

approved