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Quotients connected with the Banach matchboxes problem: Sum_{i=1..prime(n)-9} 2^(i-1)*binomial(i+3,4)/prime(n) (case 4).
8

%I #10 Mar 11 2014 18:22:39

%S 1,27,3599,29157,1362009,271400395,1469088801,201573262419,

%T 4910195172327,23758960017789,538608637491505,54480012827209187,

%U 5189654331623024397,23446625614115858667,2104894813684998321045,41392675008326544152201,182632116049323564469767

%N Quotients connected with the Banach matchboxes problem: Sum_{i=1..prime(n)-9} 2^(i-1)*binomial(i+3,4)/prime(n) (case 4).

%C See comment in A238693.

%H V. Shevelev, <a href="http://arxiv.org/abs/1110.5686">Banach matchboxes problem and a congruence for primes</a>, arXiv:1110.5686

%t k=4;(*case 4*)

%t Table[Sum[2^(i-1)Binomial[i+k-1,k],{i,p-(2k+1)}]/p,{p,Prime[Range[k+1,20]]}] (* _Peter J. C. Moses_, Mar 04 2014 *)

%Y Cf. A238693, A238697.

%K nonn

%O 5,2

%A _Vladimir Shevelev_, Mar 03 2014

%E More terms from _Peter J. C. Moses_, Mar 03 2014