A375548 a(n) is the least prime number of the form n mod (10^k) for some k > 0, or 0 if no such prime number exists.

0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 2, 3, 0, 5, 0, 7, 0, 19, 0, 0, 2, 3, 0, 5, 0, 7, 0, 29, 0, 31, 2, 3, 0, 5, 0, 7, 0, 0, 0, 41, 2, 3, 0, 5, 0, 7, 0, 0, 0, 0, 2, 3, 0, 5, 0, 7, 0, 59, 0, 61, 2, 3, 0, 5, 0, 7, 0, 0, 0, 71, 2, 3, 0, 5, 0, 7, 0, 79, 0

Offset: 0

Author

Peter Luschny, Sep 20 2024

Keywords

• nonn
• base

Crossrefs

Cf. A331097 (largest prime suffix).

Programs

Maple

mycat := (n, k) -> parse(cat(convert(n, string), convert(k, string))):
b10digs := n -> max(1, 1 + ilog10(n)): b10cat := (a, b) -> b + a * b10digs(b):
b10parts := p -> local j; [seq(irem(p, 10^(j+1)), j = 0..b10digs(p)-1)]:
b10primes := p -> local j; select(isprime, b10parts(p)):
b10maxprime := proc(n) max(b10primes(n)); ifelse(% = -infinity, 0, %) end: # A331097
b10minprime := proc(n) min(b10primes(n)); ifelse(% =  infinity, 0, %) end:
seq(b10minprime(n), n = 0..80);