A084961 Initial prime of the first prime chain of length n under the iteration x->6x+5.

2, 2, 2, 2, 11, 13, 115571, 23586221, 53165771, 3398453717, 615502598677, 32504183957101, 164289842304587

Offset: 1

Author

W. Edwin Clark, Jun 14 2003

Keywords

• more
• nonn

Comments

This is a special case of prime chains generated by f(x) = cx + d.

a(11) > 10175130529. [Donovan Johnson, Sep 27 2008]

Examples

			a(3) = 2 since 2, f(2) = 17, and f(17) = 107 are primes when f(x) = 6*x + 5.
		

Links

• D. H. Lehmer, On certain chains of primes, Proc. London Math. Soc. (3) 14a 1965 183-186.

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084956, A084957, A084958, A084959, A084960.

Programs

Mathematica

c[p_] := Block[{k=1, q=6*p+5}, While[ PrimeQ[q], q = 6*q+5; k++]; k]; a[n_] := Block[ {p=2}, While[c[p] < n, p = NextPrime[p]]; p]; Array[a, 7] (* Giovanni Resta, Mar 22 2017 *)

Extensions

a(8)-a(10) from Donovan Johnson, Sep 27 2008

a(11)-a(12) from John Cerkan, Jan 11 2017

a(13) from Giovanni Resta, Mar 22 2017