A331097 a(n) is the greatest 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, 13, 0, 5, 0, 17, 0, 19, 0, 0, 2, 23, 0, 5, 0, 7, 0, 29, 0, 31, 2, 3, 0, 5, 0, 37, 0, 0, 0, 41, 2, 43, 0, 5, 0, 47, 0, 0, 0, 0, 2, 53, 0, 5, 0, 7, 0, 59, 0, 61, 2, 3, 0, 5, 0, 67, 0, 0, 0, 71, 2, 73, 0, 5, 0, 7, 0, 79, 0

Offset: 0

Author

Rémy Sigrist, Jan 09 2020

Keywords

• nonn
• base

Comments

In other words, a(n) is the largest prime suffix of n, or 0 if no such suffix exists.

Examples

			For n = 42:
- 42 mod (10^k) = 42 is not prime for k >= 2,
- 42 mod 10 = 2 is prime,
- hence a(42) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A047814, A331044, A331102 (binary analog).

Programs

PARI

a(n,base=10) = my (d=digits(n, base), s); for (k=1, #d, if (isprime(s=fromdigits(d[k..#d], base)), return (s))); 0

Formula

a(n) <= n with equality iff n = 0 or n is a prime number.