A084959 Initial prime of a prime chain of length n under the iteration x->5x+6.

2, 5, 7, 7, 79, 79, 345431, 21171649, 34640153, 4174239239, 268130051191, 268130051191, 253134809926049, 253134809926049, 253134809926049

Offset: 1

Author

W. Edwin Clark, Jun 14 2003

Keywords

• nonn
• more

Comments

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

a(11) > 8695354111. [Donovan Johnson, Sep 27 2008]

Examples

			a(3) = 13 since 7, f(7) = 41, and f(41) = 211 are primes when f(x) = 5*x + 6.
		

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, A084960, A084961.

Programs

Mathematica

c[p_] := Block[{k=1, q = 5*p+6}, While[PrimeQ[q], q = 5*q+6; 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(7) corrected and a(8)-a(10) from Donovan Johnson, Sep 27 2008

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

a(13)-a(15) from Giovanni Resta, Mar 22 2017