A384512 Record terms in A384698.

2, 3, 13, 17, 37, 41, 61, 613, 829, 1861, 2269, 7333, 35149, 1008229, 909889549, 1423665384101, 10341624100573, 440171836495742615578609, 471206109194322691633610979351605854911441181, 4466501842784976704198682186832272945270823914876207595593007001786562643495541

Offset: 1

Author

Ya-Ping Lu, May 31 2025

Keywords

• nonn

Examples

			41 is a term because iterating the map on 12 results in a prime in 3 steps: 12 -> 2*12+1=25 -> 25-5=20 -> 2*20+1=41 and 41 is a record prime for starting integers <= 12.
		

Crossrefs

Cf. A020639 (lpf), A383777, A384698.

Programs

Python

from sympy import isprime, primefactors; rec = 1
for n in range (2, 158163):
    while not isprime(n): n = n - min(primefactors(n)) if n%2 else 2*n + 1
    if n > rec: rec = n; print(n, end = ', ')

Formula

a(n) mod 4 = 1, n > 2.