A246514 - OEIS

%I #34 Oct 22 2024 11:19:57

%S 0,1,3,4,7,9,12,14,17,22,23,27,31,33,37,41,45,48,53,56,59,63,67,72,77,

%T 80,83,87,90,94,103,107,111,113,121,124,128,134,138,144,148,150,158,

%U 160,164,166,175,184,188,190,193,199,201,209,214,219,226,228,234

%N Number of composite numbers between prime(n) and 2*prime(n) exclusive.

%H Jens Kruse Andersen, <a href="/A246514/b246514.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) + A070046(n) = number of numbers between prime(n) and 2*prime(n), which is prime(n)-1. - _N. J. A. Sloane_, Aug 28 2014

%e 2 P 4 = 0,

%e 3 4 P 6 = 1,

%e 5 6 P 8 9 10 = 3,

%e 7 8 9 10 P 12 P 14 = 4,

%e 11 12 P 14 15 16 P 18 P 20 21 22 = 7

%e and so on.

%p A246515 := proc(n) local p;  p:=ithprime(n); n - 1 + p - numtheory:-pi(2*p - 1); end; # _N. J. A. Sloane_, Oct 20 2024

%p [seq(A246515(n),n=1..120)];

%t Table[Prime[n] - PrimePi[2*Prime[n]] + n - 1, {n, 100}] (* _Paolo Xausa_, Oct 22 2024 *)

%o (PARI) s=[]; forprime(p=2, 1000, n=0; for(q=p+1, 2*p-1, if(!isprime(q), n++)); s=concat(s, n)); s \\ _Colin Barker_, Aug 28 2014

%o (PARI) a(n)=prime(n)+n-1-primepi(2*prime(n))

%o vector(100, n, a(n)) \\ Faster program. _Jens Kruse Andersen_, Aug 28 2014

%o (Python)

%o from sympy import prime, primepi

%o def A246514(n): return (m:=prime(n))+n-1-primepi(m<<1) # _Chai Wah Wu_, Oct 22 2024

%Y Related sequences:

%Y Primes (p) and composites (c): A000040, A002808, A000720, A065855.

%Y Primes between p(n) and 2*p(n): A063124, A070046; between c(n) and 2*c(n): A376761; between n and 2*n: A035250, A060715, A077463, A108954.

%Y Composites between p(n) and 2*p(n): A246514; between c(n) and 2*c(n): A376760; between n and 2*n: A075084, A307912, A307989, A376759.

%K nonn,easy

%O 1,3

%A _Odimar Fabeny_, Aug 28 2014

%E More terms from _Colin Barker_, Aug 28 2014