A323713 a(n) = beginning of a run of at least n primes when x -> 3*x - 2 is iterated.

2, 3, 3, 5, 61, 1171241, 1197631, 25451791, 25451791, 9560914721, 9560914721, 860964705721, 185133795875771

Offset: 1

Author

Jinyuan Wang, Jan 25 2019

Keywords

• nonn
• more

Comments

For n > 4, a(n) == 1 (mod 10).

Examples

			a(4) = 5 because 5 is the beginning of 4 primes in succession: 5, 3*5 - 2 = 13 is prime, 3*13 - 2 = 37 is prime, 3*37 - 2 = 109 is prime.
		

Crossrefs

Cf. A083388.

Programs

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]

PARI

a(n)={x=1;k=1;while(k==1,m=0;y=x;while(isprime(y),m++;if(m==n,k=x);y=3*y-2);x++);k;}

Extensions

a(8)-a(11) from Daniel Suteu, Jan 27 2019

a(12)-a(13) from Giovanni Resta, Feb 04 2019