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A126436
Number of composites between successive values of A014612.
3
2, 3, 0, 5, 0, 0, 8, 0, 0, 3, 1, 7, 2, 0, 1, 2, 0, 1, 10, 4, 0, 1, 1, 2, 2, 1, 0, 6, 0, 3, 5, 7, 0, 2, 0, 7, 0, 3, 0, 0, 0, 0, 4, 3, 1, 1, 2, 9, 3, 9, 4, 0, 3, 1, 1, 1, 0, 0, 7, 1, 2, 3, 1, 2, 1, 2, 1, 0, 0, 0, 3, 1
OFFSET
1,1
FORMULA
a(n) <= A114403(n) - 1.
EXAMPLE
a(1) = 2 because there are two composites {9,10} between A014612(1)=8 and A014612(2)=12.
a(2) = 3 because there are two composites {14, 15, 16} between A014612(2)=12 and A014612(3)=18.
a(3) = 0 because there are no composites between A014612(3)=18 and A014612(4)=20, only the prime 19.
a(7) = 8 because {32,33,34,35,36,38,39,40} between A014612(7)=30 and A014612(8)=42.
MAPLE
isA014612 :=proc(n) if numtheory[bigomega](n) = 3 then true ; else false ; fi ; end: isA002808 := proc(n) RETURN(not isprime(n) and n <> 1 ); end: A126436 := proc(nmax) local a ; a := -1 ; for n from 1 to nmax do if isA014612(n) then if a >= 0 then printf("%d, ", a) ; fi ; a := 0 ; elif isA002808(n) and a>= 0 then a := a+1 ; fi ; od : end: A126436(300) : # R. J. Mathar, Apr 03 2007
MATHEMATICA
nmax = 72;
S = Select[Range[300](* increase range if a(n) unevaluated *), PrimeOmega[#] == 3&];
a[n_ /; n+1 <= Length[S]] := Count[Range[S[[n]]+1, S[[n+1]]-1], _?CompositeQ];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Oct 26 2023 *)
CROSSREFS
3-almost prime analog of A046933 = number of composites between successive primes.
Sequence in context: A261781 A211402 A256064 * A102394 A145091 A085563
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 12 2007
EXTENSIONS
More terms from R. J. Mathar, Apr 03 2007
STATUS
approved