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

0,7

Comments

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

Links

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

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

Example

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

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[npd<nmax, tt=1; cp=npd+tt; While[ !(PrimeQ[cp]), tt=tt+2; cp=cp+2]; Print[tt]; n=n+1; npd=npd*Prime[n]] (* Lei Zhou, Feb 15 2005 *)

Prog

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

Crossrefs

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

Sequence in context: A108266 A102325 A231326 * A288613 A154881 A226684

Adjacent sequences: A038708 A038709 A038710 * A038712 A038713 A038714

Keyword

nonn

Author

Labos Elemer, May 02 2000

Extensions

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

Status

approved