A136612 a(n) = ((prime(n+3) + prime(n+1)) - (prime(n+2) + prime(n))).

3, 6, 4, 8, 4, 8, 8, 6, 12, 6, 8, 8, 8, 10, 8, 12, 6, 8, 10, 6, 12, 12, 10, 10, 8, 4, 8, 16, 8, 20, 6, 16, 4, 16, 8, 10, 12, 10, 8, 16, 4, 14, 4, 16, 14, 16, 14, 8, 8, 6, 16, 8, 16, 12, 8, 12, 6, 8, 14, 16, 14, 16, 8, 16, 10, 24, 8, 14, 8, 12, 12, 14, 10, 12, 12, 10, 16, 14, 10, 20, 4, 16, 6

Offset: 1

Author

Odimar Fabeny, Apr 14 2008

Keywords

• easy
• nonn

Comments

a(n) is the sum of two prime gaps, thus a(n) >= 4 for n > 1. Conjecturally a(n) << log^2 n (probably with constant around 2). - Charles R Greathouse IV, Aug 25 2014

Examples

			2 + 5 = 7
3 + 7 = 10
5 + 11 = 16
7 + 13 = 20
...
so the sequence is: 10 - 7 = 3,
16 - 10 = 6,
20 - 16 = 4,
28 - 20 = 8,
...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001223.

Programs

Maple

A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end: A136612 := proc(n) A001223(n)+A001223(n+2) ; end: seq(A136612(n),n=1..100) ; # R. J. Mathar, Apr 21 2008

Mathematica

#[[4]]+#[[2]]-#[[3]]-#[[1]]&/@Partition[Prime[Range[90]],4,1] (* Harvey P. Dale, May 15 2013 *)

PARI

a(n)=my(p=prime(n),q=nextprime(p+1),r=nextprime(q+1)); nextprime(r+1)-r + q-p \\ Charles R Greathouse IV, Aug 25 2014

Formula

a(n)=A001223(n)+A001223(n+2). - R. J. Mathar, Apr 21 2008

Extensions

Corrected and extended by R. J. Mathar, Apr 21 2008