A135283 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

We list the twin primes in staircase fashion as follows.

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).

LINKS

Table of n, a(n) for n=1..46.

FORMULA

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

PROG

(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<n, if(ispseudoprime(prime(x)+2), c++); x++; ); return(prime(x-1)) } twinu(n) = /* The n-th upper twin prime. */ { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x)) }

CROSSREFS

Sequence in context: A164407 A259216 A339867 * A225519 A213655 A119488

Adjacent sequences: A135280 A135281 A135282 * A135284 A135285 A135286

KEYWORD

nonn

AUTHOR

Cino Hilliard, Dec 02 2007

STATUS

approved