A294154 Base-2 logarithm of product of primes between 2^n+1 and 2^(n+1).

1, 1, 5, 7, 22, 39, 84, 173, 367, 716, 1444, 2945, 5823, 11817, 23457, 47117, 94496, 188670, 378296, 755437, 1512435, 3024742, 6049260, 12099777, 24205776, 48402649, 96809896, 193632363, 387252738, 774544273, 1549044943

Offset

0,3

Comments

Inspired by Bertrand's postulate and complexity of algorithms using Farey fraction sets of size 2^n.

The log of this sequence seems linear after a few terms.

Links

Table of n, a(n) for n=0..30.

Mathematica

Table[Floor[
  Log[2, Times @@
    Table[Prime[i], {i, PrimePi[2^(n)] + 1,
      PrimePi[2^(n + 1)]}]]], {n, 0, 20}]

Crossrefs

Cf. A036378 (number of primes between 2^n+1 and 2^(n+1)).

Cf. A293696, A293697 (additive view of the primes between 2^n+1 and 2^(n+1)).

Sequence in context: A350193 A248086 A076409 * A260658 A028281 A240102

Adjacent sequences: A294151 A294152 A294153 * A294155 A294156 A294157

Keyword

nonn,more

Author

Olivier Gérard, Oct 24 2017

Extensions

a(26)-a(30) from Robert Price, Nov 30 2017

Status

approved