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A133555
Order of A113709(n) among composite positive integers.
1
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
FORMULA
a(n) = A066246(A113709(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
Sequence in context: A344208 A007086 A047404 * A328727 A032938 A188323
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 25 2007
EXTENSIONS
More terms from R. J. Mathar, Jan 12 2008
STATUS
approved