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 A035346 Let F(n) = Q(n) - P(n) be the Fortunate numbers (A005235); sequence gives n such that F(n) = prime(n+1). 6
 1, 2, 3, 6, 7, 8, 14, 16, 17, 21, 73, 801, 1971, 3332, 3469, 3509, 4318, 7986 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Positive n such that A002110(n) + A000040(n+1) is prime. - Robert Israel, Dec 02 2015 Subsequence of A265109. - Altug Alkan, Dec 02 2015 LINKS Table of n, a(n) for n=1..18. Antonín Čejchan, Michal Křížek, and Lawrence Somer, On Remarkable Properties of Primes Near Factorials and Primorials, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4. S. W. Golomb, The evidence for Fortune's conjecture, Math. Mag. 54 (1981), 209-210. EXAMPLE a(10) = 21 because A002110(21) + prime(22) = 40729680599249024150621323549 = 2*3*5*...*67*71*73 + 79 is prime. MAPLE p:= 3: A[1]:= 1: count:= 1: Primorial:= 2: for n from 2 to 1000 do Primorial:= Primorial*p; p:= nextprime(p); if isprime(Primorial + p) then count:= count+1; A[count]:= n; fi od: seq(A[i], i=1..count); # Robert Israel, Dec 02 2015 MATHEMATICA Select[Range@ 801, PrimeQ[Product[Prime@ k, {k, #}] + Prime[# + 1]] &] (* Michael De Vlieger, Dec 02 2015 *) PROG (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 CROSSREFS Cf. A000040, A002110, A005235, A006862, A035345, A265109. Sequence in context: A242940 A127330 A344342 * A030164 A066646 A215488 Adjacent sequences: A035343 A035344 A035345 * A035347 A035348 A035349 KEYWORD nonn,more AUTHOR N. J. A. Sloane EXTENSIONS The terms 21 and 73 were found by Labos Elemer, May 02 2000 One more term from Ralf Stephan, Oct 20 2002 Offset changed by Altug Alkan, Dec 02 2015 Term 1971 from Michael De Vlieger, Dec 02 2015 Terms 3332, 3469, 3509, 4318, 7986 from Altug Alkan, Dec 02 2015 STATUS approved

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Last modified May 27 03:56 EDT 2024. Contains 372847 sequences. (Running on oeis4.)