A386929 a(n) is the least base b in {2,...,10} such that the base-b expansion of n, when read as a decimal integer, is prime; a(n) = 0 if no such base exists.

0, 3, 2, 3, 2, 5, 4, 5, 6, 3, 4, 9, 4, 0, 6, 5, 4, 0, 4, 0, 5, 3, 2, 0, 6, 5, 6, 5, 4, 0, 7, 0, 5, 3, 8, 0, 4, 7, 6, 0, 5, 0, 4, 0, 6, 3, 2, 9, 8, 7, 0, 7, 4, 0, 4, 5, 8, 3, 7, 0, 4, 0, 5, 9, 8, 9, 3, 5, 0, 0, 4, 0, 4, 0, 8, 0, 4, 0, 3, 0, 5, 9, 4, 9, 7, 0, 6, 9, 2, 0, 4, 0, 6, 3, 8

Offset

1,2

Comments

There are infinitely many zeros since if n is a multiple of 2520, then each base-b expansion ends with digit 0.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(2520*n) = 0.

a(630*n) = 0. - Robert Israel, Sep 09 2025

Example

a(10) = 3 since 10 in base 3 is "101" and 101 is prime; base 2 is "1010" -> 1010 composite.
a(11) = 4 since base 4 gives "23" -> 23 is prime; base 2 "1011" -> 1011 composite; base 3 "102" -> 102 composite.
a(23) = 2 since base 2 gives "10111" -> 10111 is prime.

Maple

f:= proc(n) local b, L, i;
   for b from 2 to 10 do
     L:= convert(n, base, b);
     if isprime(add(L[i]*10^(i-1), i=1..nops(L))) then return b fi
   od;
0
end proc:
map(f, [$1..100]); # Robert Israel, Sep 09 2025

Mathematica

a[n_] := Block[{m}, Do[m = FromDigits[IntegerDigits[n, b], 10]; If[PrimeQ[m], Return[b]], {b, 2, 10}]; 0]

Prog

(PARI) a(n) = for(b=2, 10, if (isprime(fromdigits(digits(n, b))), return(b))); \\ Michel Marcus, Aug 09 2025

Crossrefs

Cf. A036952 (the twos), A038537, A052026 (the zeros), A052033 (the tens).

Sequence in context: A258778 A112924 A267148 * A388299 A367682 A230406

Adjacent sequences: A386926 A386927 A386928 * A386930 A386931 A386932

Keyword

nonn,base

Author

Pietro Tiaraju Giavarina dos Santos, Aug 08 2025

Status

approved