A078731 Sum of primes between successive pairs of twin primes.

0, 0, 0, 23, 37, 100, 67, 348, 0, 371, 0, 660, 0, 0, 434, 233, 771, 277, 600, 985, 3810, 0, 1788, 3435, 2208, 1757, 1220, 631, 1300, 13190, 0, 0, 1692, 1740, 16239, 0, 1039, 0, 2156, 6678, 10749, 3745, 1283, 1297, 1307, 11040, 4319, 2930, 0, 23259, 1613, 6584

Offset: 1

Author

Reinhard Zumkeller, Dec 20 2002

Keywords

• nonn

Examples

			Between the 8th and 9th pairs of twin primes are 4 primes: (71,73) 79 83 89 97 (101,103), therefore a(8) = 79+83+89+97 = 348.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001097, A048614.

Programs

Mathematica

seq[lim_] := Module[{p = Prime[Range[lim]], d, i}, d = Differences[p]; i = Position[d, 2] // Flatten; If[First[#] + 2 >= Last[#], 0, Total[p[[First[#] + 2 ;; Last[#] - 1]]]] & /@ Partition[i, 2, 1]]; seq[300] (* Amiram Eldar, Apr 06 2025 *)