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URL: https://oeis.org/A346161

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A346161
Prime numbers p such that the number of iterations of map A039634 required for p to reach 2 sets a new record.
0
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
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
KEYWORD
nonn,more
AUTHOR
Ya-Ping Lu, Jul 08 2021
EXTENSIONS
a(19)-a(23) from Martin Ehrenstein, Aug 22 2021
STATUS
approved