A090465 Smallest number m such that n followed by m nines yields a prime or -1 if no solution exists or has been found for n.

1, 0, 0, 2, 0, -1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 2, 0, -1, 0, 2, -1, 1, 0, -1, 3, 1, -1, 4, 0, -1, 0, 2, -1, 1, 1, -1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 16, 0, -1, 1, 1, -1, 3, 0, -1, 5, 1, -1, 15, 0, -1, 0, 2, -1, 12, 1, -1, 0, 2, -1, 1, 0, -1, 0, 2, -1, 1, 3, -1, 0, 1, -1, 1, 0, -1, 1, 2, -1, 33, 0, -1, 1, 1, -1, 3, 10, -1, 0, 3, -1, 1, 0, -1, 0, 1, -1, 1, 0, -1

Offset

1,4

Comments

a(n) = 0 if n is already prime. a(n) = -1 for n = any multiple of 3 other than 3 itself. The first 9 record holders in this sequence are 1, 4, 25, 28, 46, 88, 374, 416, 466 with the values 1, 2, 3, 4, 16, 33, 57, 70, 203 respectively.

Links

Table of n, a(n) for n=1..108.

Example

a(25)=3 because three 9's must be appended to 25 before a prime is formed (25999). a(6) = -1 because no matter how many 9's are appended to 6, the resulting number is always divisible by 3 and can therefore not be prime.

Crossrefs

Cf. A083747 (The Wilde Primes, i.e. same operation using ones), A090464 (using sevens), A090584 (using threes).

Sequence in context: A343030 A246690 A317748 * A364357 A052344 A339375

Adjacent sequences: A090462 A090463 A090464 * A090466 A090467 A090468

Keyword

base,sign

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 02 2003

Status

approved