A373201 a(n) = smallest number m > 0 such that n followed by m 9's yields a prime, or -1 if no such m exists.

1, 1, -1, 2, 1, -1, 1, 1, -1, 1, 5, -1, 1, 1, -1, 2, 1, -1, 1, 2, -1, 1, 1, -1, 3, 1, -1, 4, 2, -1, 28, 2, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 16, 1, -1, 1, 1, -1, 3, 2, -1, 5, 1, -1, 15, 1, -1, 1, 2, -1, 12, 1, -1, 4, 2, -1, 1, 1, -1, 1, 2, -1, 1, 3

Offset: 1

Author

Toshitaka Suzuki, May 27 2024

Keywords

• sign
• base

Comments

a(n) = -1 when n = 3*k because no matter how many 9's are appended to n, the resulting number is always divisible by 3 and therefore cannot be prime.

a(n) = -1 when n = 37037*k + 8424, 10175, 10998, 12210, 17600, 19360, 25826, 27146, 27685, 27861, 35915 or 36047, because n followed by any positive number, m say, of 9's is divisible by at least one of the primes {7,11,13,37}.

a(4420) > 300000 or a(4420) = -1.

Examples

			a(25)=3 because 259 and 2599 are composite but 25999 is prime.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..4419

Crossrefs

Cf. A090465, A069568, A372262, A363922.