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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A054575.

Sequence in context: A033343 A128364 A281924 * A363371 A016837 A226218

Adjacent sequences: A054571 A054572 A054573 * A054575 A054576 A054577

Keyword

easy,nonn

Author

Enoch Haga, Apr 11 2000

Extensions

Corrected by Jud McCranie, Jan 04 2001

Status

approved