A084960 Initial prime of a prime chain of length n under the iteration x->5x+4.

2, 3, 5, 83, 263, 5333, 5333, 6714497, 42360737, 3757699889, 3757699889, 1431898413161, 5654774136689, 12756824771254199, 184574272412533499

Offset: 1

Author

W. Edwin Clark, Jun 14 2003

Keywords

• nonn
• hard
• more

Comments

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

Examples

			a(3) = 5 since 5, f(5) = 29 and f(29) = 149 are primes when f(x) = 5x+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, A084956, A084957, A084958, A084959, A084961.

Programs

Mathematica

t[p_] := Block[{c=1, q = 5*p+4}, While[ PrimeQ@q, q = 5*q + 4; c++]; c]; a[n_] := Block[{p = 2}, While[t[p] < n, p = NextPrime@ p]; p]; Array[a, 8] (* Giovanni Resta, Mar 21 2017 *)

Extensions

a(9) from Stefan Steinerberger, May 18 2007

a(10)-a(11) from Donovan Johnson, Sep 27 2008

a(12)-a(13) from Giovanni Resta, Mar 21 2017

a(14)-a(15) from Bert Dobbelaere, May 30 2025