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A294154 Base-2 logarithm of product of primes between 2^n+1 and 2^(n+1). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A036498 A248086 A076409 * A260658 A028281 A240102

Adjacent sequences:  A294151 A294152 A294153 * A294155 A294156 A294157

KEYWORD

nonn,more,changed

AUTHOR

Olivier Gérard, Oct 24 2017

EXTENSIONS

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

STATUS

approved

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Last modified April 17 09:29 EDT 2021. Contains 343064 sequences. (Running on oeis4.)