A380312 - OEIS

%I #16 Jan 24 2025 23:20:08

%S 19,29,37,67,73,101,131,167,181,197,211,241,251,257,317,389,421,463,

%T 479,503,523,599,643,653,691,719,739,811,827,859,887,907,919,941,983,

%U 1039,1061,1069,1109,1117,1217,1277,1283,1289,1307,1361,1381,1427,1429,1499

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

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

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

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

%o (PARI) \\ This will loop forever if it hits a loop other than 3 or 19, but if it returns the result is correct.

%o gpf(n)=my(f=factor(n)[,1]); f[#f]

%o is(p)=while(p>28, p=gpf(2*p-1)); p==19 \\ _Charles R Greathouse IV_, Jan 24 2025

%Y Cf. A006530, A023583.

%K easy,nonn

%O 1,1

%A _Johannes M.V.A. Koelman_, Jan 20 2025