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

Offset

0,1

Links

Table of n, a(n) for n=0..22.

Example

a(1) = 4 since the primes 5, 7, 11 and 13 lie between 4 and 16.

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

Prog

(C) #include <stdio.h> #include <inttypes.h> int main (void) { int64_t n1=1; int64_t n2=1; int i; int64_t sum=0, next; printf("%lld, %lld, ", n1, n2); for (i=0; i<12; i++) { next=n1*n2-sum; sum+=n1; n1=n2; n2=next; printf("%lld, ", n2); } }
(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

Crossrefs

Cf. A036378.

Sequence in context: A273955 A054542 A214198 * A009623 A148208 A245798

Adjacent sequences: A117754 A117755 A117756 * A117758 A117759 A117760

Keyword

nonn

Author

Greg Huber, Apr 14 2006

Extensions

More terms from Brian Kuehn (brk158(AT)psu.edu), Apr 19 2006

Status

approved