|
Search: id:A108197
|
|
|
| A108197 |
|
Number of composite numbers between two successive semiprimes. |
|
+0
1
|
|
| 0, 1, 0, 1, 0, 3, 0, 1, 0, 4, 0, 0, 1, 0, 4, 1, 1, 2, 1, 0, 1, 2, 2, 2, 2, 3, 1, 0, 0, 2, 1, 0, 0, 7, 2, 2, 2, 0, 1, 0, 0, 4, 2, 0, 4, 0, 0, 1, 0, 6, 1, 0, 1, 3, 1, 6, 0, 2, 1, 1, 4, 4, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 0, 1, 3, 5, 1, 7, 1, 2, 0, 3, 2, 1, 1, 4, 2, 6, 1, 1, 2, 2, 0, 1, 0, 0, 1, 2, 2, 3, 1, 1, 2, 0, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
COMMENT
|
This is to A046933 as semiprimes A001358 are to primes A000040. This is to composites A002808 as A088700 is to primes. a(A070552(i)) = 0. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 10 2007
a(n) = 0 if A001358(n) is in A070552. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 11 2007
|
|
FORMULA
|
a(n) = A065855(A001358(n+1)) - A065855(A001358(n)) - 1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2007
a(n)=A065516(n)-1-A088700(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008]
|
|
EXAMPLE
|
a(1) = 0 because between 2*2 and 2*3 there is 5 and it is not composite.
a(2) = 1 because between 2*3 and 3*3 there is 8 = 2*2*2;
a(6) = 3 because between 3*5 and 3*7 there are three composite numbers: {16, 18, 20}.
a(10) = 4 because between 2*13 and 3*11 there are four composite numbers: {27, 28, 30, 32}.
a(15) = 4 because there are four composites {40,42,44,45} between semiprime(15)=39 and semiprime(16)=46.
|
|
MAPLE
|
with(numtheory): sp:=proc(n) if bigomega(n)=2 then n else fi end: SP:=[seq(sp(n), n=1..450)]: for j from 1 to nops(SP)-1 do ct:=0: for i from SP[j]+1 to SP[j+1]-1 do if isprime(i)=false then ct:=ct+1 else ct:=ct fi: od: a[j]:=ct: od:seq(a[j], j=1..nops(SP)-1); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2007
A001358 := proc(nmin) local a, n ; a :=[] ; n := 1 ; while nops(a) < nmin do if numtheory[bigomega](n) = 2 then a := [op(a), n] ; fi ; n := n+1 ; od: RETURN(a) ; end: A000720 := proc(n) numtheory[pi](n) ; end: A065855 := proc(n) n-A000720(n)-1 ; end: A108197 := proc(nmin) local a, n, a001358 ; a001358 := A001358(nmin+1) ; a := [] ; for n from 1 to nops(a001358)-1 do a := [op(a), A065855(op(n+1, a001358))-A065855(op(n, a001358))-1 ] ; od; RETURN(a) ; end: A108197(100) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2007
|
|
CROSSREFS
|
Semiprime analogue of A046933.
Cf. A001358, A002808, A046933, A065855, A070552, A088700.
Adjacent sequences: A108194 A108195 A108196 this_sequence A108198 A108199 A108200
Sequence in context: A035640 A079327 A123878 this_sequence A049769 A117179 A111526
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Jun 15 2005
|
|
EXTENSIONS
|
Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 07 2005
Edited by njas at the suggestion of Andrew Plewe, Jul 13 2007
Further edited by njas at the suggestion of R. J. Mathar, Jul 01 2008
|
|
|
Search completed in 0.005 seconds
|
