A238698 Quotients connected with the Banach matchboxes problem: Sum_{i=1..prime(n)-9} 2^(i-1)*binomial(i+3,4)/prime(n) (case 4).

1, 27, 3599, 29157, 1362009, 271400395, 1469088801, 201573262419, 4910195172327, 23758960017789, 538608637491505, 54480012827209187, 5189654331623024397, 23446625614115858667, 2104894813684998321045, 41392675008326544152201, 182632116049323564469767

Offset: 5

Author

Vladimir Shevelev, Mar 03 2014

Keywords

• nonn

Comments

See comment in A238693.

Links

• V. Shevelev, Banach matchboxes problem and a congruence for primes, arXiv:1110.5686

Crossrefs

Cf. A238693, A238697.

Programs

Mathematica

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

Extensions

More terms from Peter J. C. Moses, Mar 03 2014