A383777 -id:A383777 - cp's OEIS frontend

A384698 The first prime number reached by iterating the map, x -> 2*x + 1 if x is even; x - lpf(x) otherwise where lpf(x) is the least prime factor of x, on n >= 2; or -1 if a prime is never reached.

2, 3, 13, 5, 13, 7, 17, 13, 37, 11, 41, 13, 29, 41, 61, 17, 37, 19, 41, 37, 613, 23, 613, 41, 53, 613, 109, 29, 61, 31, 829, 61, 1861, 61, 73, 37, 277, 73, 157, 41, 613, 43, 89, 613, 181, 47, 97, 613, 101, 97, 401, 53, 109, 101, 113, 109, 229, 59, 829, 61, 241

Offset: 2

Ya-Ping Lu, Jun 09 2025

nonn

Conjecture: a(n) != -1.

			a(4) = 13 because iterating the map on n = 4 reaches a prime, 13, in three steps: 4 -> 2*4+1=9 -> 9-3=6 -> 2*6+1=13.

Cf. A020639 (lpf), A383777.

from sympy import isprime, primefactors
for n in range (2, 63):
    while not isprime(n): n = n - min(primefactors(n)) if n%2 else 2*n + 1
    print(n, end = ', ')

a(n) = n if n is a prime; > n otherwise.

a(n) mod 4 = 1 unless n is a prime and n mod 4 = 3.

A384512 Record terms in A384698.

Original entry on oeis.org

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.

cp's OEIS Frontend

A384698 The first prime number reached by iterating the map, x -> 2*x + 1 if x is even; x - lpf(x) otherwise where lpf(x) is the least prime factor of x, on n >= 2; or -1 if a prime is never reached.

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