A117757 Number of primes between 4^n and 4^(n+1).
2, 4, 12, 36, 118, 392, 1336, 4642, 16458, 59025, 213922, 781924, 2879938, 10673034, 39769185, 148880193, 559658890, 2111459404, 7991867657, 30336822624, 115457945437, 440455347499, 1683882372217, 6450190109521, 24752190739937, 95142124007068, 366264701294309, 1411989176124066
Offset: 0
Keywords
Examples
a(1) = 4 since the primes 5, 7, 11 and 13 lie between 4 and 16.
Links
- Amiram Eldar, Table of n, a(n) for n = 0..45
Programs
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Maple
a:=proc(n) local ct,j: ct:=0: for j from 4^n to 4^(n+1) do if isprime(j)=true then ct:=ct+1 else fi: ct: od: end: seq(a(n),n=0..8); # execution takes hours - Emeric Deutsch, Apr 16 2006
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PARI
{ for(n=0,30, istrt=4^n ; iend=istrt*4 ; resul=0 ; forprime(p=istrt+1,iend, resul++ ; ) ; print1(resul,",") ; ) ; } \\ R. J. Mathar, Apr 21 2006 -
PARI
a(n) = primepi(4^(n+1)) - primepi(4^n) \\ Michel Marcus, Jun 21 2013
Extensions
More terms from Brian Kuehn (brk158(AT)psu.edu), Apr 19 2006
a(23)-a(27) from Amiram Eldar, Jun 11 2024