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

Author

Rémy Sigrist, Jan 08 2020

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

See A331045 for a similar sequence.

Cf. A039634, A202259, A320584.

Programs

Mathematica

A331044[n_] := NestWhile[Quotient[#, 10] &, n, # > 0 && !PrimeQ[#] &];
Array[A331044, 100, 0] (* Paolo Xausa, Nov 22 2024 *)

PARI

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

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.