A238697 Quotients connected with the Banach matchboxes problem: Sum_{i=1..prime(n)-7} 2^(i-1)*binomial(i+2,3)/prime(n) (case 3).

0, 19, 197, 10481, 64027, 1980327, 259179061, 1257208799, 131286703021, 2756321451033, 12473384091267, 250290955437775, 21588599628845597, 1792050990708087027, 7763319803561678613, 620323392829436218475, 11365013042482773469559, 48487140450183407727097

Offset: 4

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 [math.HO], 2011.

Crossrefs

Cf. A238693.

Programs

Mathematica

Array[Sum[2^(i - 1)*Binomial[i + 2, 3]/#, {i, # - 7}] &@ Prime@ # &, 18, 4] (* Michael De Vlieger, Dec 06 2018 *)

PARI

a(n) = sum(i=1, prime(n)-7, 2^(i-1)*binomial(i+2,3))/prime(n); \\ Michel Marcus, Dec 06 2018

Extensions

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