A176881 a(n)=p-q for n-th product of 2 distinct primes p and q (q

1, 3, 5, 2, 4, 9, 11, 8, 15, 2, 17, 10, 21, 14, 6, 16, 27, 29, 8, 20, 35, 4, 39, 12, 41, 26, 6, 28, 45, 14, 51, 34, 18, 57, 10, 59, 38, 40, 12, 65, 44, 69, 2, 24, 71, 26, 77, 50, 16, 81, 56, 87, 58, 32, 6, 95, 64, 99, 22, 36, 101, 8, 68, 105, 38, 24, 107, 70, 4, 111, 42, 76, 6, 80

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 27 2010

Keywords

• nonn

Comments

Where products of two distinct primes are in A006881.

If Polignac's conjecture is true, then every even positive integer occurs infinitely many times in this sequence. - Clark Kimberling, Apr 25 2016

Examples

			a(1)=1 because 1=3-2 for A006881(1)=6=3*2; a(2)=3 because 3=5-2 for A006881(2)=10=5*2.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006881, A096916, A070647.

Programs

Maple

A006881 := proc(n) if n = 1 then 6; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 and nops(numtheory[factorset](a)) =2 then return a; end if; end do: end if; end proc:
A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
for n from 1 to 130 do c := A006881(n) ; printf("%d,",A006530(c)-A020639(c)) ; end do:
# R. J. Mathar, May 01 2010

Mathematica

mx = 350; t = Sort@Flatten@Table[Prime[n]*Prime[m], {n, Log[2, mx/3]}, {m, n + 1, PrimePi[mx/Prime[n]]}]; (* A006881, Robert G.Wilson v, Feb 07 2012 *)
u = Table[FactorInteger[t[[k]]][[1]], {k, 1, Length[t]}];
u1 = Table[u[[k]][[1]], {k, 1, Length[t]}]  (* A096916 *)
PrimePi[u1]  (* A270650 *)
v = Table[FactorInteger[t[[k]]][[2]], {k, 1, Length[t]}];
v1 = Table[v[[k]][[1]], {k, 1, Length[t]}]  (* A070647 *)
PrimePi[v1]  (* A270652 *)
d = v1 - u1  (* A176881 *)  (* Clark Kimberling, Apr 25 2016 *)

Extensions

Entries checked by R. J. Mathar, May 01 2010