A098168 - OEIS

%I #12 May 22 2022 14:32:25

%S 2,3,4,6,9,7,8,9,12,18,19,18,20,15,28,17,18,29,24,27,22,36,45,26,27,

%T 51,48,31,48,43,38,50,117,52,37,39,85,52,46,43,46,76,51,133,65,137,

%U 111,65,76,62,86,67,61,59,58,79,63,67,75,94,67,64,78,67,71,81,82,153,101,221

%N Prime index j such that prime(j) = the n-th fortunate number, A005235(n).

%H Antonín Čejchan, Michal Křížek, and Lawrence Somer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Krizek/krizek3.html">On Remarkable Properties of Primes Near Factorials and Primorials</a>, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4.

%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]; Table[ PrimePi[ Fortunate[n]], {n, 70}] (* _Robert G. Wilson v_, Sep 04 2004 *)

%Y Cf. A005235, A055211, A098166, A098167.

%K nonn

%O 1,1

%A _Pierre CAMI_, Aug 30 2004

%E More terms from _Robert G. Wilson v_, Sep 04 2004

%E Better definition from _R. J. Mathar_, Oct 28 2007