A277434 Primes in A001075.

2, 7, 97, 708158977

Offset: 1

Author

Timothy L. Tiffin, Oct 14 2016

Keywords

• nonn
• hard

Comments

For n >= 2, a(n) == 7 mod 30.

Terms in this sequence have the form A001075(2^k) [see my third comment on A001075]: a(1) = A001075(2^0) = A001075(1), a(2) = A001075(2^1) = A001075(2), a(3) = A001075(2^2) = A001075(4), and a(4) = A001075(2^4) = A001075(16). Are there more terms and, if so, will a(5) = A001075(2^16) = A001075(65536)?

The following terms are not prime and, thus, not in the sequence: A001075(m), for m = 8, 32, 64, 128, 256, 512, 1024. So, a(5) > 2.3619*10^585.

a(5), if it exists, is at least A001075(2^23) and hence has more than four million decimal digits. - Charles R Greathouse IV, Nov 10 2016

Links

• D. Alpern, Factorization using the Elliptic Curve Method.

Crossrefs

Cf. A001075.

Programs

Mathematica

Select[LinearRecurrence[{4, -1}, {1, 2}, 30], PrimeQ] (* Michael De Vlieger, Oct 21 2016, after Harvey P. Dale at A001075 *)

PARI

lista(nn) =  for (n=0, nn, if (isprime(p=polchebyshev(n,1,2)), print1(p, ", "))); \\ Michel Marcus, Oct 21 2016

PFGW

ABC2 Linear(1, 2, 7, 26, 2^$a)
a: from 1 to 25
Charles R Greathouse IV, Nov 07 2016