This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376761 #27 Jul 09 2025 05:06:41 %S A376761 2,2,2,3,4,4,3,4,5,4,4,5,6,6,6,6,7,7,7,7,7,8,8,9,9,9,10,10,9,10,10,9, %T A376761 10,10,11,12,12,13,13,14,14,13,12,12,13,13,14,13,14,15,14,13,14,15,15, %U A376761 15,15,15,16,16,16,16,17,17,17,18,18,18,18,18,19,19,20,21,20,19,19,20,19,18,18,19,19,20,20,21,21,21,22,23,23,23,23,23,24,23,24,24,24,24,24,25 %N A376761 Number of primes between the n-th composite number c(n) and 2*c(n). %C A376761 Obviously the endpoints are not counted (since they are composite). %H A376761 N. J. A. Sloane, <a href="/A376761/b376761.txt">Table of n, a(n) for n = 1..20000</a> %F A376761 a(n) = A000720(2*A002808(n)) - A002808(n) + n + 1. - _Paolo Xausa_, Oct 22 2024 %t A376761 MapIndexed[PrimePi[2*#] + #2[[1]] - # + 1 &, Select[Range[100], CompositeQ]] (* _Paolo Xausa_, Oct 22 2024 *) %o A376761 (Python) %o A376761 from sympy import composite, primepi %o A376761 def A376761(n): return n+1-(m:=composite(n))+primepi(m<<1) # _Chai Wah Wu_, Oct 22 2024 %Y A376761 Related sequences: %Y A376761 Primes (p) and composites (c): A000040, A002808, A000720, A065855. %Y A376761 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 A376761 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 A376761 nonn %O A376761 1,1 %A A376761 _N. J. A. Sloane_, Oct 22 2024