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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 20 08:54 EDT 2021. Contains 343125 sequences. (Running on oeis4.)