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%I #12 Mar 28 2015 22:46:55
%S 3,8,15,28,51,68,87,110,147,208,275,336,407,454,561,620,681,790,879,
%T 982,1061,1212,1409,1510,1613,1846,2069,2196,2419,2610,2773,3002,3645,
%U 3884,4041,4208,4647,4886,5085,5276,5475,5858,6091,6842,7155,7928,8535,8848
%N a(n) = Sum_{i=1..n} A005235(i).
%C The primes and fortunate numbers in the partial sum of the fortunate numbers (A005235): primes begin: 3, 1061, 1409, 1613, 2069, 6091; fortunate numbers in partial sum begin: 3, 1061, 1409, 1613, 6091, and these subsequences are not disjoint. [_Jonathan Vos Post_, Jan 27 2010]
%F Let F(n) := a(n)/A007504(n). Conjecture: as n tends to infinity F(n) tends to Pi/2 with Pi=3.14159......
%t NextPrime[ n_Integer] := Block[{k}, k = n + 1; While[ !PrimeQ[ k ], k++ ]; k ]; Fortunate[ n_Integer] := Block[{p = Product[ Prime[i], {i, 1, n} ] + 1, q}, q = NextPrime[p]; q - p + 1 ]; t = Table[ Fortunate[ n ], {n, 1, 48}]; Table[Plus @@ Take[t, n], {n, 48}] (* _Robert G. Wilson v_, Sep 04 2004 *)
%t Accumulate[NextPrime[#]-#+1&/@(Rest[FoldList[Times,1,Prime[Range[ 60]]]]+ 1)] (* _Harvey P. Dale_, May 27 2014 *)
%Y Cf. A005235 A007504.
%K nonn
%O 1,1
%A _Pierre CAMI_, Aug 29 2004
%E More terms from _Robert G. Wilson v_, Sep 04 2004
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