A036378 Number of primes p between powers of 2, 2^n < p <= 2^(n+1).
1, 1, 2, 2, 5, 7, 13, 23, 43, 75, 137, 255, 464, 872, 1612, 3030, 5709, 10749, 20390, 38635, 73586, 140336, 268216, 513708, 985818, 1894120, 3645744, 7027290, 13561907, 26207278, 50697537, 98182656, 190335585, 369323305, 717267168, 1394192236, 2712103833
Offset: 0
Keywords
Examples
The 7 primes for which A029837(p)=6 are 37, 41, 43, 47, 53, 59, 61.
Links
- Ray Chandler, Table of n, a(n) for n = 0..91 (using data from A007053; n = 0..74 by T. D. Noe, n = 75..85 by Gord Palameta, n = 86..89 by David Baugh)
- Paul D. Beale, A new class of scalable parallel pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers, arXiv:1411.2484 [physics.comp-ph], 2014-2015.
- Paul D. Beale and Jetanat Datephanyawat, Class of scalable parallel and vectorizable pseudorandom number generators based on non-cryptographic RSA exponentiation ciphers, arXiv:1811.11629 [cs.CR], 2018.
- Seung-Hoon Lee, Mario Gerla, Hugo Krawczyk, Kang-Won Lee, and Elizabeth A. Quaglia, Performance Evaluation of Secure Network Coding using Homomorphic Signature, 2011 International Symposium on Networking Coding.
- Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
Programs
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Magma
[1,1] cat [#PrimesInInterval(2^n, 2^(n+1)): n in [2..29]]; // Vincenzo Librandi, Nov 18 2014
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Mathematica
t = Table[PrimePi[2^n], {n, 0, 20}]; Rest@t - Most@t (* Robert G. Wilson v, Mar 20 2006 *) -
PARI
a(n) = primepi(1<<(n+1))-primepi(1<
Formula
a(n) = primepi(2^(n+1)) - primepi(2^n).
a(n) = A095005(n)+A095006(n) = A095007(n) + A095008(n) = A095013(n) + A095014(n) = A095015(n) + A095016(n) (for n > 1) = A095021(n) + A095022(n) + A095023(n) + A095024(n) = A095019(n) + A095054(n) = A095020(n) + A095055(n) = A095060(n) + A095061(n) = A095063(n) + A095064(n) = A095094(n) + A095095(n).
Extensions
More terms from Labos Elemer, May 13 2004
Entries checked by Robert G. Wilson v, Mar 20 2006
Comments