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 A108197 Number of composite numbers between two successive semiprimes. 2
 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; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS 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, Oct 10 2007 a(n) = 0 if A001358(n) is in A070552. - Jonathan Vos Post, Mar 11 2007 LINKS Table of n, a(n) for n=1..105. FORMULA a(n) = A065855(A001358(n+1)) - A065855(A001358(n)) - 1. - R. J. Mathar, Oct 23 2007 a(n)=A065516(n)-1-A088700(n). - R. J. Mathar, 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, 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, Oct 23 2007 MATHEMATICA terms = 105; cc = Select[Range[4 terms], CompositeQ] /. c_ /; PrimeOmega[c] == 2 -> 0; SequenceReplace[cc, {0, c___ /; FreeQ[{c}, 0]} :> Length[{c}]][[;; terms]] (* Jean-François Alcover, Mar 31 2020 *) CROSSREFS Semiprime analog of A046933. Cf. A001358, A002808, A046933, A065855, A070552, A088700. Sequence in context: A238342 A123878 A284148 * A318455 A363029 A049769 Adjacent sequences: A108194 A108195 A108196 * A108198 A108199 A108200 KEYWORD easy,nonn AUTHOR Giovanni Teofilatto, Jun 15 2005 EXTENSIONS Corrected and extended by Ray Chandler, Jul 07 2005 Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 13 2007 Further edited by N. J. A. Sloane at the suggestion of R. J. Mathar, Jul 01 2008 STATUS approved

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Last modified May 20 02:34 EDT 2024. Contains 372703 sequences. (Running on oeis4.)