A340418 Indices in A339991 where records occur.

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

Offset

1,2

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.

Links

Table of n, a(n) for n=1..16.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A083771 A158069 A039726 * A115617 A003064 A057429

Adjacent sequences: A340415 A340416 A340417 * A340419 A340420 A340421

Keyword

nonn,more

Author

Ya-Ping Lu, Jan 06 2021

Status

approved