A084956 Initial prime of the first prime chain of length n under the iteration x -> 3x+4.

2, 3, 3, 23, 3203, 34613, 165443, 1274803, 26314573, 26314573, 590256673403, 15113026057043, 334156170011893, 3998669569752373

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) = 3 since 3, f(3) = 13 and f(13) = 43 are primes when f(x) = 3*x + 4.
		

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, A084957, A084958, A084959, A084960, A084961.

Programs

Mathematica

c[p_] := Block[{k=1, q=3*p + 4}, While[PrimeQ[q], q=3*q+4; 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(9)-a(10) from Donovan Johnson, Sep 27 2008

a(11)-a(12) from John Cerkan, Jan 13 2017

a(13)-a(14) from Giovanni Resta, Mar 22 2017