cp's OEIS Frontend

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

%I A016104 #32 Apr 17 2025 07:00:10
%S A016104 1,3,13,16381
%N A016104 2^2^2^ ... 2^w (with n 2's), where w = 1.92878... = A086238.
%C A016104 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
%C A016104 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]
%D A016104 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 137-138.
%H A016104 Robert Baillie, <a href="https://arxiv.org/abs/1705.09741">Wright's Fourth Prime</a>, arXiv:1705.09741 [math.NT], 2017.
%H A016104 Aminu Alhaji Ibrahim and Sa’idu Isah Abubaka, <a href="http://dx.doi.org/10.4236/apm.2016.66028">Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties</a>, Advances in Pure Mathematics, 2016, 6, 409-419.
%H A016104 Simon Plouffe, <a href="https://arxiv.org/abs/2002.12137">The calculation of p(n) and pi(n)</a>, arXiv:2002.12137 [math.NT], 2020.
%H A016104 Paulo Ribenboim, <a href="http://www.maa.org/programs/maa-awards/writing-awards/prime-number-records">Prime number records</a>, Two-Year College Math. Jnl., 25 (1994), pp. 280-290.
%H A016104 Juan L. Varona, <a href="https://arxiv.org/abs/2012.11750">A Couple of Transcendental Prime-Representing Constants</a>, arXiv:2012.11750 [math.NT], 2020.
%H A016104 E. M. Wright, <a href="http://www.jstor.org/stable/2306356">A prime-representing function</a>, Amer. Math. Monthly, 58 (1951), 616-618.
%F A016104 a(0) = 1, a(n) = the greatest prime less than 2^(a(n-1)+1). - _Charles R Greathouse IV_, Oct 25 2006
%Y A016104 Cf. A086238.
%K A016104 nonn
%O A016104 0,2
%A A016104 _Robert G. Wilson v_