A038711 a(n) is the smallest m such that A002110(n) + m is prime.

1, 1, 1, 1, 1, 1, 17, 19, 23, 37, 61, 1, 61, 71, 47, 107, 59, 61, 109, 89, 103, 79, 151, 197, 101, 103, 233, 223, 127, 223, 191, 163, 229, 643, 239, 157, 167, 439, 239, 199, 191, 199, 383, 233, 751, 313, 773, 607, 313, 383, 293, 443, 331, 283, 277, 271, 401, 307

Offset: 0

Author

Labos Elemer, May 02 2000

Keywords

• nonn

Comments

Any composite a(n) would disprove Fortune's conjecture, see A005235. - Jeppe Stig Nielsen, Oct 31 2003

Examples

			For n=11, 1 + A002110(11) = 200560490131 < 200560490197 = 67 + A002110(11); therefore, a(11)=1 but A005235(11)=67.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002110, A005235, A035345, A018239, A038710, A060270.

Programs

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
a:= n-> nextprime(p(n))-p(n):
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 16 2020

Mathematica

nmax=2^16384; npd=1;n=1;npd=npd*Prime[n]; While[npdLei Zhou, Feb 15 2005 *)

PARI

a(n) = my(P=vecprod(primes(n))); nextprime(P+1) - P; \\ Michel Marcus, Dec 12 2023

Formula

a(n) = Min(1, A005235(n)); a(n)=1 for n=1, 2, 3, 4, 5, 11, 75, ...

a(n) = 1 for n=0, 1, 2, 3, 4, 5, 11, 75, ... (A014545); a(n) = A005235(n) otherwise. - Jeppe Stig Nielsen, Oct 31 2003

a(n) = A038710(n) - A002110(n). - Alois P. Heinz, Mar 16 2020

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 16 2020