A054574 Begin with n-th prime, add its prime divisors (itself), repeat until reach a new prime; sequence gives prime reached.

23, 11, 17, 23, 47, 41, 53, 59, 71, 89, 167, 113, 269, 131, 167, 191, 179, 227, 239, 263, 251, 239, 251, 269, 293, 431, 311, 359, 383, 383, 383, 479, 479, 419, 449, 881, 2039, 491, 503, 521, 2039, 659, 2039, 743, 593, 599, 839, 743, 683, 911, 701, 719, 1103

Offset: 1

Author

Enoch Haga, Apr 11 2000

Keywords

• easy
• nonn

Comments

Prime factors are counted with multiplicity. - Sean A. Irvine, Feb 07 2022

Examples

			a(5)=47 because starting with the 5th prime, 11: 11+11=22; 22+2+11=35; 35+5+7=47, a prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054575.

Programs

Mathematica

f[n_] := n + Plus @@ Times @@@ FactorInteger@n; a[n_] := NestWhile[f, (p = Prime[n]), # == p || CompositeQ[#] &]; Array[a, 100] (* Amiram Eldar, Sep 07 2019 *)

Extensions

Corrected by Jud McCranie, Jan 04 2001