A133555 - OEIS

%I #18 Jul 24 2024 02:05:10

%S 1,2,3,6,9,10,11,14,19,24,27,28,29,32,37,42,47,48,51,56,57,60,71,74,

%T 75,76,79,82,95,96,99,104,105,114,119,124,125,128,133,138,147,148,151,

%U 152,157,168,175,178,181,182,187,196,197,202,207,212,217,220,221,228,231

%N Order of A113709(n) among composite positive integers.

%F a(n) = A066246(A113709(n)). - _R. J. Mathar_, Jan 12 2008

%e The 10th prime - the 9th prime = 29-23 = 6. The integer between 23 and 29 that is divisible by 6 is 24. 24 is the 14th composite, so a(9) = 14.

%p A113709 := proc(n) local d,a ; d := ithprime(n+1)-ithprime(n) ; for a from ithprime(n)+1 do if a mod d = 0 then RETURN(a) ; fi ; od: end: A066246 := proc(n) local a,i; if n = 1 or isprime(n) then 0 ; else a := 0 ; for i from 4 to n do if not isprime(i) then a := a+1 ; fi ; od: RETURN(a) ; fi ; end: A133555 := proc(n) A066246(A113709(n)) ; end: seq(A133555(n),n=2..80) ; # _R. J. Mathar_, Jan 12 2008

%t compositePi[n_] := n - PrimePi[n] - 1;

%t a[n_] := Module[{p1 = Prime[n], p2 = Prime[n+1], c}, c = SelectFirst[ Range[p1+1, p2-1], Divisible[#, p2-p1]&]; compositePi[c]];

%t Table[a[n], {n, 2, 62}] (* _Jean-François Alcover_, Apr 02 2024 *)

%Y Cf. A066246, A113709.

%K nonn

%O 2,2

%A _Leroy Quet_, Dec 25 2007

%E More terms from _R. J. Mathar_, Jan 12 2008