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

Author

Dmitri Kamenetsky, Oct 01 2012

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A040081.