A016104 2^2^2^ ... 2^w (with n 2's), where w = 1.92878... = A086238.

1, 3, 13, 16381

Offset: 0

Author

Robert G. Wilson v

Keywords

• nonn

Comments

w is uniquely defined as the largest value such that for all n>0, a(n) is prime. - Charles R Greathouse IV, Oct 25 2006

Wright's paper uses this as an example, although the sequence is not well-defined there. The next term is probably 2^16382-35411, a 4932-digit prp. - Charles R Greathouse IV, Oct 25 2006 [Update March 2019: Samuel S. Wagstaff, Jr proves the primality of a(4), see the Baillie link for details. - Charles R Greathouse IV, Mar 27 2019]

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 137-138.

Links

• Robert Baillie, Wright's Fourth Prime, arXiv:1705.09741 [math.NT], 2017.
• Aminu Alhaji Ibrahim and Sa’idu Isah Abubaka, Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties, Advances in Pure Mathematics, 2016, 6, 409-419.
• Simon Plouffe, The calculation of p(n) and pi(n), arXiv:2002.12137 [math.NT], 2020.
• Paulo Ribenboim, Prime number records, Two-Year College Math. Jnl., 25 (1994), pp. 280-290.
• Juan L. Varona, A Couple of Transcendental Prime-Representing Constants, arXiv:2012.11750 [math.NT], 2020.
• E. M. Wright, A prime-representing function, Amer. Math. Monthly, 58 (1951), 616-618.

Crossrefs

Cf. A086238.

Formula

a(0) = 1, a(n) = the greatest prime less than 2^(a(n-1)+1). - Charles R Greathouse IV, Oct 25 2006