A133555 Order of A113709(n) among composite positive integers.

1, 2, 3, 6, 9, 10, 11, 14, 19, 24, 27, 28, 29, 32, 37, 42, 47, 48, 51, 56, 57, 60, 71, 74, 75, 76, 79, 82, 95, 96, 99, 104, 105, 114, 119, 124, 125, 128, 133, 138, 147, 148, 151, 152, 157, 168, 175, 178, 181, 182, 187, 196, 197, 202, 207, 212, 217, 220, 221, 228, 231

Offset

2,2

Links

Table of n, a(n) for n=2..62.

Formula

a(n) = A066246(A133709(n)). - R. J. Mathar, Jan 12 2008

Example

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.

Maple

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

Mathematica

compositePi[n_] := n - PrimePi[n] - 1;
a[n_] := Module[{p1 = Prime[n], p2 = Prime[n+1], c}, c = SelectFirst[ Range[p1+1, p2-1], Divisible[#, p2-p1]&]; compositePi[c]];
Table[a[n], {n, 2, 62}] (* Jean-François Alcover, Apr 02 2024 *)

Crossrefs

Cf. A066246, A113709.

Sequence in context: A344208 A007086 A047404 * A328727 A032938 A188323

Adjacent sequences: A133552 A133553 A133554 * A133556 A133557 A133558

Keyword

nonn

Author

Leroy Quet, Dec 25 2007

Extensions

More terms from R. J. Mathar, Jan 12 2008

Status

approved