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 A294154 #17 Nov 23 2024 18:14:31
%S A294154 1,1,5,7,22,39,84,173,367,716,1444,2945,5823,11817,23457,47117,94496,
%T A294154 188670,378296,755437,1512435,3024742,6049260,12099777,24205776,
%U A294154 48402649,96809896,193632363,387252738,774544273,1549044943
%N A294154 Base-2 logarithm of product of primes between 2^n+1 and 2^(n+1).
%C A294154 Inspired by Bertrand's postulate and complexity of algorithms using Farey fraction sets of size 2^n.
%C A294154 The log of this sequence seems linear after a few terms.
%t A294154 Table[Floor[
%t A294154 Log[2, Times @@
%t A294154 Table[Prime[i], {i, PrimePi[2^(n)] + 1,
%t A294154 PrimePi[2^(n + 1)]}]]], {n, 0, 20}]
%Y A294154 Cf. A036378 (number of primes between 2^n+1 and 2^(n+1)).
%Y A294154 Cf. A293696, A293697 (additive view of the primes between 2^n+1 and 2^(n+1)).
%K A294154 nonn,more
%O A294154 0,3
%A A294154 _Olivier Gérard_, Oct 24 2017
%E A294154 a(26)-a(30) from _Robert Price_, Nov 30 2017