A331044 a(n) is the greatest 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, 23, 2, 2, 2, 2, 2, 29, 3, 31, 3, 3, 3, 3, 3, 37, 3, 3, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 5, 5, 5, 53, 5, 5, 5, 5, 5, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 7, 71, 7, 73, 7, 7, 7, 7, 7, 79, 0

Offset

0,3

Comments

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

This sequence is a decimal variant of A039634.

Links

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

Formula

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

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

Example

For n = 42:
- neither 42 nor 4 is a prime number,
- hence a(42) = 0.
For n = 290:
- 290 is not a prime number,
- 29 is a prime number,
- hence a(290) = 29.

Prog

(PARI) a(n, base=10) = while (n, if (isprime(n), return (n), n\=base)); 0

Crossrefs

See A331045 for a similar sequence.

Cf. A039634, A202259, A320584.

Sequence in context: A269668 A061397 A331045 * A093438 A375548 A211396

Adjacent sequences: A331041 A331042 A331043 * A331045 A331046 A331047

Keyword

nonn,base

Author

Rémy Sigrist, Jan 08 2020

Status

approved