A035346 Let F(n) = Q(n) - P(n) be the Fortunate numbers (A005235); sequence gives n such that F(n) = prime(n+1).

1, 2, 3, 6, 7, 8, 14, 16, 17, 21, 73, 801, 1971, 3332, 3469, 3509, 4318, 7986, 41292

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..19.

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

a(10)-a(11) were found by Labos Elemer, May 02 2000

a(12) from Ralf Stephan, Oct 20 2002

Offset changed by Altug Alkan, Dec 02 2015

a(13) from Michael De Vlieger, Dec 02 2015

a(14)-a(18) from Altug Alkan, Dec 02 2015

a(19) from Henri Lifchitz, Nov 08 2024

Status

approved