A340418 Indices in A339991 where records occur.

1, 2, 3, 5, 7, 11, 19, 29, 39, 53, 61, 73, 79, 101, 149, 229

Offset: 1

Author

Ya-Ping Lu, Jan 06 2021

Keywords

• nonn
• more

Comments

The records in A339991 corresponding the first 16 terms in this sequence are 0, 1, 4, 8, 9, 15, 22, 23, 24, 31, 32, 71, 88, 99, 104, 9267.

A339991(397), which is > 249275, is still unknown.

A339991(397) > 10^6. - Michael S. Branicky, Jan 09 2025

Crossrefs

Cf. A339991, A340008, A060412 (Collatz record indices).

Programs

Mathematica

With[{s = Array[-1 + Length@ NestWhileList[Which[EvenQ@ #, #/2, PrimeQ@ #, #^2 - 1, True, # - 1] &, #, # > 1 &] &, 396]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Feb 12 2021 *)

Python

from sympy import isprime
rec = -1
for n in range(1, 397):
    m, ct = n, 0
    while m > 1:
        if m%2 == 0: m //= 2
        elif isprime(m) == 1: m = m*m - 1
        else: m -= 1
        ct += 1
    if ct > rec: print(n); rec = ct