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A135283 Sum of staircase twin primes according to the rule: top + bottom + next top. 3
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.

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).

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: A164494 A164407 A259216 * A225519 A213655 A119488

Adjacent sequences:  A135280 A135281 A135282 * A135284 A135285 A135286

KEYWORD

nonn

AUTHOR

Cino Hilliard, Dec 02 2007

STATUS

approved

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Last modified June 26 02:24 EDT 2017. Contains 288749 sequences.