A084958 Initial prime of a prime chain of length n under the iteration x->5x+2.

2, 3, 13, 19, 373, 135859, 135859, 18235423, 26588257, 93112729, 376038903103, 7087694466289, 120223669028389

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) > 8695354111. - Donovan Johnson, Sep 27 2008

Examples

			a(3)=13 since 13, f(13)=67 and f(67)=337 are primes when f(x) = 5x+2.
		

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, A084959, A084960, A084961.

Programs

Mathematica

c[p_] := Block[{k = 1, q = 5*p+2}, While[ PrimeQ[q], q = 5*q+2; k++]; k]; a[n_] := Block[{p = 2}, While[c[p] < n, p = NextPrime@ p]; p]; Array[a, 7] (* Giovanni Resta, Mar 21 2017 *)

Extensions

a(10) from Donovan Johnson, Sep 27 2008

a(11)-a(12) from John Cerkan, Jan 20 2017

a(13) from Giovanni Resta, Mar 21 2017