A331045 a(n) is the least prime number of the form floor(n/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, 0, 13, 0, 0, 0, 17, 0, 19, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 83

Offset: 0

Author

Rémy Sigrist, Jan 08 2020

Keywords

• nonn
• base

Comments

In other words, a(n) is the least prime prefix of n, or 0 if every prefix of n is nonprime.

This sequence is a variant of A331044.

Examples

			For n = 23:
- 2 is a prime number,
- hence a(23) = 2.
		

Links

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

Crossrefs

Cf. A069090, A202259, A331044.

Programs

PARI

a(n, base=10) = my (d=digits(n, base), p=0); for (k=1, #d, if (isprime(p=base*p+d[k]), return (p))); return (0)

Formula

a(n) <= n with equality iff n = 0 or n belongs to A069090.

a(n) >= 0 with equality iff n belongs to A202259.

a(n) <= A331044(n).