|
Search: id:A065890
|
|
|
| A065890 |
|
Number of composites less than the n-th prime. |
|
+0
6
|
|
| 0, 0, 1, 2, 5, 6, 9, 10, 13, 18, 19, 24, 27, 28, 31, 36, 41, 42, 47, 50, 51, 56, 59, 64, 71, 74, 75, 78, 79, 82, 95, 98, 103, 104, 113, 114, 119, 124, 127, 132, 137, 138, 147, 148, 151, 152, 163, 174, 177, 178, 181, 186, 187, 196, 201, 206, 211, 212, 217, 220, 221
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
First differences form A046933, which requires that for this sequence the parity of successive terms alternates.
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,1000
|
|
FORMULA
|
a(n) = A000040(n)-n-1 = A014689(n)-1 = A014692(n)-2
|
|
EXAMPLE
|
p = p(25) = 97 is th 25th prime,p-1 = 96 is the 71st composite number in A002808; it is also the 72nd nonprime in A018252; A065890(n) = composite [in A002808] index of p(n)-1; A014689(n) = composite [in A002808] index of p(n)+1; A014689(n) = nonprime [in A018252] index of p(n)-1; A014692(n) = nonprime [in A018252] index of p(n)+1.
|
|
MATHEMATICA
|
CompositePi[n_Integer] := (n - PrimePi[n] - 1); Table[ CompositePi[ Prime[n]], {n, 1, 75} ]
|
|
PROGRAM
|
(PARI) { for (n=1, 1000, p=prime(n); a=p - primepi(p) - 1; write("b065890.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 03 2009]
|
|
CROSSREFS
|
Cf. A000040, A014689, A014692, A002808, A018252, A065855, A046933.
Sequence in context: A166097 A000277 A003664 this_sequence A162177 A078632 A122701
Adjacent sequences: A065887 A065888 A065889 this_sequence A065891 A065892 A065893
|
|
KEYWORD
|
nonn,new
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 28 2001
|
|
|
Search completed in 0.002 seconds
|
