A167595 The number of nonisolated primes between the n-th nonisolated nonprime and the n-th isolated nonprime.

1, 2, 1, 3, 5, 5, 7, 9, 9, 11, 13, 15, 17, 19, 21, 23, 23, 25, 27, 29, 31, 33, 35, 37, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 61, 63, 65, 67, 69, 71, 73, 75, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 119

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 06 2009

Keywords

• nonn
• easy

Examples

			a(1)=1  (0 < 3 < 4);
a(2)=2  (1 < 3,5 < 6);
a(3)=1  (8 < 11 <12);
a(4)=3  (9 < 11,13,17 < 18);
a(5)=5 (10 < 11,13,17,19,29 < 30);
a(6)=5 (14 < 17,19,29,31,41 < 42);
a(7)=7 (15 < 17,19,29,31,41,43,59 < 60);
a(8)=9 (16 < 17,19,29,31,41,43,59,61,71 < 72).
		

Crossrefs

Cf. A001097 (the nonisolated primes), A014574 (the isolated nonprimes), A164276 (the nonisolated nonprimes), A167511.

Programs

Maple

A164276 := proc(n) option remember; if n = 1 then 0; else for a from procname(n-1)+1 do if isA164276(a) then return a; end if; end do; end if: end proc:
A001097 := proc(n) option remember; if n =1 then 3; else for a from procname(n-1)+2 by 2 do if isA001097(a) then return a; end if; end do: end if; end proc:
A167595 := proc(n) a := 0 ; for k from A164276(n)+1 to A014574(n)-1 do if isA001097(k) then a := a+1 ; end if; end do: a ; end proc:
seq(A167595(n),n=1..120) ; # R. J. Mathar, May 30 2010

Extensions

More terms from R. J. Mathar, May 30 2010