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

Author

Pietro Tiaraju Giavarina dos Santos, Aug 08 2025

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

a(2520*n) = 0.