A084957 Initial prime of the first prime chain of length n under the iteration x -> 4x + 3.

2, 2, 2, 2, 1447, 9769, 17231, 17231, 32611, 18527009, 161205841, 3123824801, 26813406071, 4398156030379, 4398156030379

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) = c*x + d.

Examples

			a(3) = 2 since 2, f(2) = 11, and f(11) = 47 are primes when f(x) = 4*x + 3.
		

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, A084958, A084959, A084960, A084961.

Programs

Mathematica

c[p_] := Block[{k=1, q=4*p+3}, While[ PrimeQ[q], q=4*q+3; k++]; k]; a[n_] := Block[ {p=2}, While[c[p] < n, p = NextPrime@ p]; p]; Array[a, 9] (* Giovanni Resta, Mar 21 2017 *)

PARI

has(p,n)=for(i=2,n, if(!isprime(p=4*p+3), return(0))); 1
a(n)=forprime(p=2,, if(has(p,n), return(p))) \\ Charles R Greathouse IV, Jan 20 2017

Extensions

a(11)-a(12) from Donovan Johnson, Sep 27 2008

a(13) from John Cerkan, Jan 20 2017

a(14)-a(15) from Giovanni Resta, Mar 21 2017