A384698 -id:A384698 - cp's OEIS frontend

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

Ya-Ping Lu, May 31 2025

nonn

			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.

Cf. A020639 (lpf), A383777, A384698.

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 = ', ')

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

A384874 a(n) is the first prime encountered when iterating the map x -> x/2 if x is even, x*lpf(x) + 1 otherwise, where lpf(x) is the least prime factor of x, on n >= 2; or -1 if a prime is never reached.

Original entry on oeis.org

2, 3, 2, 5, 3, 7, 2, 7, 5, 11, 3, 13, 7, 23, 2, 17, 7, 19, 5, 2, 11, 23, 3, 313, 13, 41, 7, 29, 23, 31, 2, 313, 17, 11, 7, 37, 19, 59, 5, 41, 2, 43, 11, 17, 23, 47, 3, 43, 313, 5869, 13, 53, 41, 13, 7, 43, 29, 59, 23, 61, 31, 313, 2, 163, 313, 67, 17, 13, 11

Offset: 2

Ya-Ping Lu, Jun 11 2025

nonn

Conjecture: a(n) != -1.

For n <= 24, this sequence is the same as A320028.

Ya-Ping Lu, Table of n, a(n) for n = 2..1000
Ya-Ping Lu, A plot of a(n) for n <= 1000

Cf. A006370, A320028, A384698.

from sympy import isprime, primefactors
def A384874(n):
    while not isprime(n): n = n*min(primefactors(n))+1 if n%2 else n//2
    return n

cp's OEIS Frontend

A384512 Record terms in A384698.

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