A086757 Smallest prime p such that n is a palindrome in base-p representation.

2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 13, 5, 3, 13, 2, 3, 2, 5, 23, 3, 2, 23, 3, 5, 29, 3, 2, 3, 31, 29, 2, 7, 2, 37, 37, 5, 41, 37, 41, 3, 5, 13, 47, 43, 2, 5, 53, 7, 53, 7, 2, 3, 59, 17, 59, 3, 5, 59, 61, 11, 67, 5, 2, 7, 2, 67, 5, 3, 71, 13, 7, 5, 2, 73, 79, 37, 79, 5, 83, 3, 83, 3, 5, 11, 2

Offset: 1

Author

Reinhard Zumkeller, Aug 01 2003

Keywords

• nonn
• base

Comments

A016026(n) <= a(n) <= A007918(n).

Crossrefs

Cf. A007918, A016026.

Cf. A006995 (a(n)=2).

Programs

PARI

isok(p,n) = my(d=digits(n,p)); d == Vecrev(d);
a(n) = my(p=2); while (!isok(p,n), p=nextprime(p+1)); p; \\ Michel Marcus, Jan 30 2024

Python

from sympy import sieve
from sympy.ntheory import is_palindromic
def a086757(n): return next(p for p in sieve if is_palindromic(n, p)) # Dumitru Damian, Jan 29 2024