%I #48 May 22 2022 13:59:42
%S 1,2,3,6,7,8,14,16,17,21,73,801,1971,3332,3469,3509,4318,7986
%N Let F(n) = Q(n) - P(n) be the Fortunate numbers (A005235); sequence gives n such that F(n) = prime(n+1).
%C Positive n such that A002110(n) + A000040(n+1) is prime. - _Robert Israel_, Dec 02 2015
%C Subsequence of A265109. - _Altug Alkan_, Dec 02 2015
%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.
%H S. W. Golomb, <a href="http://www.jstor.org/stable/2689634">The evidence for Fortune's conjecture</a>, Math. Mag. 54 (1981), 209-210.
%e a(10) = 21 because A002110(21) + prime(22) = 40729680599249024150621323549 = 2*3*5*...*67*71*73 + 79 is prime.
%p p:= 3:
%p A[1]:= 1:
%p count:= 1:
%p Primorial:= 2:
%p for n from 2 to 1000 do
%p Primorial:= Primorial*p;
%p p:= nextprime(p);
%p if isprime(Primorial + p) then
%p count:= count+1;
%p A[count]:= n;
%p fi
%p od:
%p seq(A[i],i=1..count); # _Robert Israel_, Dec 02 2015
%t Select[Range@ 801, PrimeQ[Product[Prime@ k, {k, #}] + Prime[# + 1]] &] (* _Michael De Vlieger_, Dec 02 2015 *)
%o (PARI) lista(nn) = {s = 1; for(k=1, nn, s *= prime(k); if(ispseudoprime(s + prime(k+1)), print1(k, ", ")); ); } \\ _Altug Alkan_, Dec 02 2015
%Y Cf. A000040, A002110, A005235, A006862, A035345, A265109.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_
%E The terms 21 and 73 were found by _Labos Elemer_, May 02 2000
%E One more term from _Ralf Stephan_, Oct 20 2002
%E Offset changed by _Altug Alkan_, Dec 02 2015
%E Term 1971 from _Michael De Vlieger_, Dec 02 2015
%E Terms 3332, 3469, 3509, 4318, 7986 from _Altug Alkan_, Dec 02 2015