A380312 Primes not reaching 3 under iterations of p -> gpf(2*p-1).

19, 29, 37, 67, 73, 101, 131, 167, 181, 197, 211, 241, 251, 257, 317, 389, 421, 463, 479, 503, 523, 599, 643, 653, 691, 719, 739, 811, 827, 859, 887, 907, 919, 941, 983, 1039, 1061, 1069, 1109, 1117, 1217, 1277, 1283, 1289, 1307, 1361, 1381, 1427, 1429, 1499

Offset: 1

Author

Johannes M.V.A. Koelman, Jan 20 2025

Keywords

• easy
• nonn

Comments

It appears that this is the primes reaching 19 under iterations of p -> gpf(2*p-1).

Conjecture: a(n) ~ k*n log n for some constant k. Perhaps k ≈ 4.51. - Charles R Greathouse IV, Jan 24 2025

Examples

			19, 37, 73 and 29 are in the sequence as they form a loop under the iteration.
		

Crossrefs

Cf. A006530, A023583.

Programs

PARI

\\ This will loop forever if it hits a loop other than 3 or 19, but if it returns the result is correct.
gpf(n)=my(f=factor(n)[,1]); f[#f]
is(p)=while(p>28, p=gpf(2*p-1)); p==19 \\ Charles R Greathouse IV, Jan 24 2025