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%I #5 Sep 10 2016 15:54:25
%S 13,23,41,65,101,143,191,245,311,353,425,479,551,581,623,695,749,821,
%T 875,971,1115,1271,1325,1445,1613,1739,1817,1877,1943,2129,2441,2471,
%U 2513,2597,2783,3071,3113,3161,3215,3335,3533,3737,3845,3881,3923,4067
%N Sum of staircase twin primes according to the rule: top + bottom + next top.
%C We list the twin primes in staircase fashion as follows.
%C 3
%C 5_5
%C __7_11
%C ____13_17
%C _______19_29
%C __________31_41
%C _____________.._..
%C ________________tu(n)_tl(n)
%C ______________________tu(n+1)
%C ...
%C 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).
%F a(n) = A054735(n)+A001359(n+1). - _R. J. Mathar_, Sep 10 2016
%o (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)) }
%K nonn
%O 1,1
%A _Cino Hilliard_, Dec 02 2007
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