A135283 Sum of staircase twin primes according to the rule: top + bottom + next top.

13, 23, 41, 65, 101, 143, 191, 245, 311, 353, 425, 479, 551, 581, 623, 695, 749, 821, 875, 971, 1115, 1271, 1325, 1445, 1613, 1739, 1817, 1877, 1943, 2129, 2441, 2471, 2513, 2597, 2783, 3071, 3113, 3161, 3215, 3335, 3533, 3737, 3845, 3881, 3923, 4067

Offset: 1

Author

Cino Hilliard, Dec 02 2007

Keywords

• nonn

Comments

We list the twin primes in staircase fashion as follows.

3

5_5

__7_11

____13_17

_______19_29

__________31_41

___________.._..

________________tu(n)_tl(n)

______________________tu(n+1)

...

where tl(n) = n-th lower twin prime, tu(n) = n-th upper twin prime. Then a(n) = tl(n) + tu(n) + tl(n+1).

Programs

PARI

g(n) = for(x=1,n,y=twinu(x)+twinl(x) + twinl(x+1);print1(y",")) twinl(n) = / *The n-th lower twin prime. */ { local(c,x); c=0; x=1; while(c
				

Formula

a(n) = A054735(n)+A001359(n+1). - R. J. Mathar, Sep 10 2016