A083388 a(n) = beginning of a run of at least n primes when x -> 3*x + 2 is iterated.

2, 3, 5, 29, 1129, 10009, 575119, 32694619, 586130089, 1030544269, 427744892959, 18736892249459, 221530676461709, 221530676461709

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..14.

D. H. Lehmer, On certain chains of primes, Proc. London Math. Soc. (3) 14a 1965 183-186.

Example

a(3) = 5 because 5 is the beginning of 3 primes in succession: 5, 3*5 + 2 = 17 is prime and 3*17 + 2 = 53 is prime.

Mathematica

c[p_] := Block[{k=1, q = 3 p + 2}, While[PrimeQ[q], q = 3 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 *)

Prog

(PARI) mx=1; forprime(p=1, 198000, x=p; m=0; while(isprime(x=3*x+2), m=m+1; if(m>mx, print(p, " ", m, " ", x); mx=m, ))) \\ Donald S. McDonald, Jun 11 2003

Crossrefs

Cf. A057331, A081173.

Sequence in context: A073309 A226124 A110389 * A090475 A060301 A040119

Adjacent sequences: A083385 A083386 A083387 * A083389 A083390 A083391

Keyword

nonn

Author

W. Edwin Clark, Jun 09 2003

Extensions

a(8)-a(10) from Donovan Johnson, Sep 27 2008

a(11)-a(12) from John Cerkan, Jan 09 2017

a(13)-a(14) from Giovanni Resta, Mar 21 2017

Status

approved