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

1,1

Comments

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

Links

Table of n, a(n) for n=1..13.

Example

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.

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]

Prog

(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; }

Crossrefs

Cf. A083388.

Sequence in context: A154646 A355868 A046826 * A054892 A104570 A103356

Adjacent sequences: A323710 A323711 A323712 * A323714 A323715 A323716

Keyword

nonn,more

Author

Jinyuan Wang, Jan 25 2019

Extensions

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

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

Status

approved