A346161 Prime numbers p such that the number of iterations of map A039634 required for p to reach 2 sets a new record.

2, 3, 7, 23, 47, 191, 383, 1439, 2879, 11519, 23039, 261071, 1044287, 2949119, 31426559, 194224127, 1069493759, 8554807007, 31337349119, 68438456063, 136876912127, 547507648511, 8760122376191

Offset: 1

Author

Ya-Ping Lu, Jul 08 2021

Keywords

• nonn
• more

Comments

It seems that the record number of iterations for a(n) is n-1.

Alternatively, prime numbers p such that the number of odd primes encountered under iteration of A004526 sets a new record. - Martin Ehrenstein, Aug 16 2021

Examples

			Terms in this sequence are indicated in square brackets in the tree below for primes up to 97. Note that a(n) is the smallest prime of depth n-1.
                 1                 ___________[2]____________
                 |                /        /   |   \    \    \
         _______[3]__       ____ 5 _     17   19   37   67   73
        /        |   \     /     |  \     |    |
     _[7]_      13   97   11    41  43   71   79
    /  |  \      |       /  \    |
  29  31  61    53    [23]  89  83
   |                    |
  59                  [47]
		

Crossrefs

Cf. A005384, A058000, A039634, A346063, A346163.

Programs

Python

from sympy import nextprime, isprime
rec = -1; p1 = 1
while p1 < 1000000000:
    p = nextprime(p1); m = p; ct = 0
    while m > 2:
        if isprime(m): ct += 1
        m //= 2
    if ct > rec: print(p); rec = ct
    p1 = p

Extensions

a(19)-a(23) from Martin Ehrenstein, Aug 22 2021