A089750 a(n) = the first prime in the orbit of n under f(n) = n + the first prime > n, or 0 if no such prime exists.

3, 2, 3, 43, 5, 13, 7, 19, 43, 379, 11, 113, 13, 31, 18749, 2341, 17, 37, 19, 43, 379, 788941, 23, 53, 113, 241, 511213, 4089763, 29, 61, 31, 18749, 2341, 71, 601, 73, 37, 79, 163, 331, 41, 353, 43, 379, 788941, 403941973, 47, 101, 13499, 103, 211

Offset

1,1

Comments

Note that a(n) = n when n is prime.

Question: Is a(n) > 0 for all n? I do not have a value for a(46).

a(46)=403941973, a(52)=31626333786385669717. - Michel Marcus, May 19 2013

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

4 -> 4 + (first prime > 4) = 4 + 5 = 9 -> 9 + 11 = 20 -> 20 + 23 = 43 (prime). So a(4) = 43.

Maple

f:= proc(n) local k;
  k:= n;
  while not isprime(k) do k:= k + nextprime(k) od;
  k
end proc:
map(f, [$1..100]); # Robert Israel, Sep 04 2018

Mathematica

a[n_] := NestWhile[# + NextPrime[#]&, n, CompositeQ];
Array[a, 100] (* Jean-François Alcover, Aug 26 2020 *)

Prog

(PARI) a(n) = {while(! isprime(n), n = n + nextprime(n+1); ); return (n); } \\ Michel Marcus, May 19 2013

Crossrefs

Sequence in context: A248244 A139170 A139075 * A109591 A143932 A304496

Adjacent sequences: A089747 A089748 A089749 * A089751 A089752 A089753

Keyword

nonn

Author

Joseph L. Pe, Jan 08 2004

Extensions

More terms from Michel Marcus, May 19 2013

Status

approved