A217377 a(n) is the smallest m>=0 such that ((5n+1)*6^m-1)/5 is prime; or -1 if no such value exists.

1, 0, 0, 2, 0, 1, 0, 4, 2, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 2, 1, 4, 0, 3, 1, 1, 1, 3, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 3, 1, 0, 15, 0, 3, 1, 1, 0, 4, 3, 3008, 1, 1, 0, 2, 1, 1, 4, 1, 0, 3, 0, 1, 1, 2, 2, 1, 0, 1, 3, 1, 0, 1, 0, 2, 2, 1, 1, 4, 0, 2, 1, 4, 0, 5, 2, 8

Offset

1,4

Comments

Let f(n)=6n+1. Let f(n,m) be f applied to n m-times. For example f(n,3) = f(f(f(n))). Then a(n) is the smallest m>=0 such that f(n,m) is prime.

a(525)=27871 is the largest found value in this sequence, which generates a probable prime with 21691 digits.

a(1247) and a(1898) are currently unknown. If they are positive then a(1247)>86500 and a(1898)>58000.

Links

Dmitri Kamenetsky, Table of n, a(n) for n = 1..1246

Example

a(8)=4, because 4 is the smallest value for m such that ((5*8+1)*6^m-1)/5 is prime. The prime value is (41*6^4-1)/5 = 6*(6*(6*(6*8+1)+1)+1)+1 = 10627.

Crossrefs

Cf. A040081.

Sequence in context: A067631 A134317 A123641 * A361652 A362834 A362839

Adjacent sequences: A217374 A217375 A217376 * A217378 A217379 A217380

Keyword

nonn

Author

Dmitri Kamenetsky, Oct 01 2012

Status

approved