A135275 a(n) = prime(2n-1) + prime(2n) - prime(2n+1).

0, 1, 7, 13, 21, 27, 37, 41, 53, 65, 69, 75, 95, 101, 95, 121, 127, 143, 153, 161, 169, 187, 185, 207, 223, 231, 235, 251, 263, 275, 269, 305, 299, 321, 343, 345, 361, 373, 385, 391, 409, 425, 433, 445, 457, 459, 479, 493, 507, 517

Offset: 1

Author

Cino Hilliard, Dec 02 2007

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A096379, A135274.

Programs

Mathematica

Table[Prime[n + 1] + Prime[n] - Prime[n + 2], {n, 1, 30}][[;; ;; 2]] (* G. C. Greubel, Oct 08 2016 *)

PARI

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

PARI

n=1; p=2; q=3; forprime(r=5,1e3, if(n, print1(p+q-r", ")); n=!n; p=q; q=r) \\ Charles R Greathouse IV, Oct 08 2016

Formula

We list the primes in staircase fashion as in A135274. 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).

a(n) = A096379(2*n-1). - R. J. Mathar, Sep 10 2016

Extensions

New name from Charles R Greathouse IV, Oct 08 2016