A268061 Numbers k such that 7*8^k - 1 is prime.

3, 7, 15, 59, 6127, 8703, 11619, 23403, 124299

Offset: 1

Author

Robert Price, Jan 25 2016

Keywords

• nonn
• hard
• more

Comments

a(10) > 2*10^5.

Terms are A001771(n)/3 that are integers.

References

• R. K. Guy, Unsolved Problems in Theory of Numbers, Section A3.

Links

• H. C. Williams, The primality of certain integers of the form 2Ar^n - 1, Acta Arith. 39 (1981), 7-17.

Crossrefs

Cf. similar sequences of the form k*(k+1)^n-1: A003307 (k=2), ... (k=3), A046865 (k=4), A079906 (k=5), A046866 (k=6), this sequence (k=7), ... (k=8), A056725 (k=9), A046867 (k=10), A079907 (k=11).

Cf. A001771, A002235, A005541, A247260.

Programs

Mathematica

Select[Range[0, 200000], PrimeQ[7*8^# - 1] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime(7*8^n-1), print1(n, ", "))) \\ Altug Alkan, Jan 25 2016