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
Keywords
Examples
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.
Links
- D. H. Lehmer, On certain chains of primes, Proc. London Math. Soc. (3) 14a 1965 183-186.
Programs
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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 *) -
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
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
Comments