This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A122834 #23 Feb 16 2025 08:33:02 %S A122834 3,5,7,13,17,19,31,61,67,127,257,1021,4093,4099,8191,16381,65537, %T A122834 65539,131071,262147,524287,1048573,4194301,16777213,268435459, %U A122834 1073741827,2147483647,2305843009213693951,19342813113834066795298819 %N A122834 Primes in the new Mersenne conjecture; odd primes of the form 2^k+-1 or 4^k+-3. %C A122834 Let p be a prime in this sequence. Call q=2^p-1 and r=(2^p+1)/3. The new Mersenne conjecture implies that either q and r are both prime or both composite. %D A122834 R. K. Guy, Unsolved Problems in Number Theory, Section A3. %H A122834 Gord Palameta, <a href="/A122834/b122834.txt">Table of n, a(n) for n = 1..40</a> %H A122834 P. T. Bateman, J. L. Selfridge, and S. S. Wagstaff, Jr., <a href="http://www.jstor.org/stable/2323195">The New Mersenne Conjecture</a>, Amer. Math. Monthly 96, 125-128, 1989. %H A122834 John Renze and Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NewMersennePrimeConjecture.html">MathWorld: New Mersenne Prime Conjecture</a>. %t A122834 nn=100; Union[Select[1+2^Range[16],PrimeQ], Select[ -1+2^Range[2nn],PrimeQ], Select[3+4^Range[nn],PrimeQ], Select[ -3+4^Range[nn],PrimeQ]] %Y A122834 Superset of: A000668, A019434, A228026. %Y A122834 Cf. A000043 (n such that 2^n-1 is prime), A000978 (n such that (2^n+1)/3 is prime), A107360 (the intersection of these). %K A122834 nonn %O A122834 1,1 %A A122834 _T. D. Noe_, Sep 12 2006