A080220 a(1)=2; then if n is prime, a(n) is the smallest prime number greater than a(n-1), if n is composite a(n)=a(n-1)+1.

2, 3, 5, 6, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 97

Offset

1,1

Comments

More generally, let b(1)>1, m >0, b(n) be the smallest integer > b(n-1) such that b(n) is prime if n is prime, then limit n ->infinity b(n)/n =L exists and b<L<b+1.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

There is a constant C such that limit n ->infinity a(n)/n = C =1.72...

Mathematica

nxt[{n_, a_}]:={n+1, If[PrimeQ[n+1], NextPrime[a], a+1]}; NestList[nxt, {1, 2}, 80][[;; , 2]] (* Harvey P. Dale, Sep 13 2024 *)

Prog

(PARI) a(n)=if(n<2, 2, if(isprime(n), nextprime(a(n-1)+1), a(n-1)+1))

Crossrefs

Sequence in context: A161873 A224517 A341534 * A028778 A284885 A094180

Adjacent sequences: A080217 A080218 A080219 * A080221 A080222 A080223

Keyword

nonn

Author

Benoit Cloitre, Feb 06 2003

Status

approved