A090584 Smallest number m such that n followed by m threes yields a prime or -1 if no solution exists or has been found for n.

1, 0, 0, 1, 0, -1, 0, 1, -1, 1, 0, -1, 0, 2, -1, 1, 0, -1, 0, 3, -1, 1, 0, -1, 8, 1, -1, 1, 0, -1, 0, 4, -1, 2, 1, -1, 0, 1, -1, 483, 0, -1, 0, 1, -1, 1, 0, -1, 2, 1, -1, 1, 0, -1, 3, 1, -1, 6, 0, -1, 0, 5, -1, 1, 1, -1, 0, 1, -1, 5, 0, -1, 0, 1, -1, 3, 1, -1, 0, 4, -1, 1, 0, -1, 1, 1, -1, 1, 0, -1, 2, 3, -1, 2, 1, -1, 0, 1, -1, 3, 0, -1, 0, 2, -1, 1, 0, -1, 0, 1

Offset

1,14

Comments

a(n) = 0 if n is already prime. a(n) = -1 for n = any multiple of 3 other than 3 itself. The first 5 record holders in this sequence are 1, 14, 20, 25, 40 with the values 1, 2, 3, 8, 483 respectively. 410 may be the next record holder as no solution has been found for it yet. 410 was tested out to 1250 threes with no prime formed.

Links

Table of n, a(n) for n=1..110.

Example

a(25)=8 because eight 3's must be appended to 25 before a prime is formed (2533333333). a(6) = -1 because no matter how many 3'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), A090465 (using nines).

Sequence in context: A019269 A204459 A035155 * A171400 A271592 A357187

Adjacent sequences: A090581 A090582 A090583 * A090585 A090586 A090587

Keyword

base,sign

Author

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

Status

approved