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

1,1

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

Links

Table of n, a(n) for n=1..23.

Example

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]

Prog

(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

Crossrefs

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

Sequence in context: A037231 A248525 A366929 * A082449 A129741 A006720

Adjacent sequences: A346158 A346159 A346160 * A346162 A346163 A346164

Keyword

nonn,more

Author

Ya-Ping Lu, Jul 08 2021

Extensions

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

Status

approved