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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
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
Sequence in context: A242940 A127330 A344342 * A030164 A066646 A215488
KEYWORD
nonn,more
AUTHOR
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.)