This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340418 #19 Jun 17 2025 20:17:18
%S A340418 1,2,3,5,7,11,19,29,39,53,61,73,79,101,149,229
%N A340418 Indices in A339991 where records occur.
%C A340418 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.
%C A340418 A339991(397), which is > 249275, is still unknown.
%C A340418 A339991(397) > 10^6. - _Michael S. Branicky_, Jan 09 2025
%t A340418 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 *)
%o A340418 (Python)
%o A340418 from sympy import isprime
%o A340418 rec = -1
%o A340418 for n in range(1, 397):
%o A340418 m, ct = n, 0
%o A340418 while m > 1:
%o A340418 if m%2 == 0: m //= 2
%o A340418 elif isprime(m) == 1: m = m*m - 1
%o A340418 else: m -= 1
%o A340418 ct += 1
%o A340418 if ct > rec: print(n); rec = ct
%Y A340418 Cf. A339991, A340008, A060412 (Collatz record indices).
%K A340418 nonn,more
%O A340418 1,2
%A A340418 _Ya-Ping Lu_, Jan 06 2021