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

0,3

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.

Links

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

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).

Example

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

Prog

(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)

Crossrefs

Cf. A069090, A202259, A331044.

Sequence in context: A071375 A269668 A061397 * A331044 A093438 A211396

Adjacent sequences: A331042 A331043 A331044 * A331046 A331047 A331048

Keyword

nonn,base

Author

Rémy Sigrist, Jan 08 2020

Status

approved