A135274 a(n) = prime(2*n) - prime(2*n-1) + prime(2*n+1).

6, 13, 19, 25, 37, 47, 49, 65, 69, 77, 89, 103, 107, 113, 131, 141, 151, 159, 173, 185, 193, 199, 213, 239, 235, 247, 267, 275, 279, 287, 317, 317, 335, 353, 355, 373, 385, 393, 409, 427, 433, 441, 453, 469, 469, 499, 503, 513, 535, 565

Offset: 1

Author

Cino Hilliard, Dec 02 2007

Keywords

• nonn
• easy

Comments

Original name was: Difference and sum of staircase primes according to the rule: bottom - top + next top.

We list the primes in staircase fashion as follows.

2

3.5

..7.11

....13.17

.......19.23

..........29.31

.............37.41

.....................

....................n

....................n+1.n+2.

The right diagonal, RD(n), is the set of top primes and the left diagonal, LD(x), is the set of bottom primes. Then a(n) = LD(n+1) - RD(n) + RD(n+2).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Join[{6},#[[3]]-#[[2]]+#[[4]]&/@Partition[Prime[Range[2,110]],4,2]] (* Harvey P. Dale, Nov 16 2011 *)

PARI

g(n) = forstep(x=1,n,2,y=prime(x+1)-prime(x)+prime(x+2);print1(y","))

PARI

a(n)=prime(2*n)-prime(2*n-1)+prime(2*n+1); \\ Joerg Arndt, Oct 08 2016

Formula

a(n) = A181428(2*n-1). - R. J. Mathar, Sep 10 2016

Extensions

New name from Joerg Arndt, Oct 08 2016