A388263 Indices of records of A388038.

1, 2, 3, 5, 10, 20, 40, 77, 154, 308, 616, 1232, 1357, 2714, 5428, 10856, 21712, 43424, 86848, 157005, 314010, 628020, 746829, 1008973, 2017946, 4035892, 8071784, 16143568, 32287136, 64574272, 129148544

Offset

1,2

Comments

See comment in A388262 regarding computation of A388263(24)-A388263(30). - Michael S. Branicky, Sep 21 2025

Links

Table of n, a(n) for n=1..31.

Michael S. Branicky, List of k, Indices, Values of A388038(k) for ties of record values <= 3584971550.

Formula

a(n) <= 2*a(n-1), since A388038(2k) = 1 + A388038(k).

Mathematica

r = -1; Monitor[Reap[Do[q = 1; If[# > r, r = #; Sow[n]] &[-1 + Length@ NestWhileList[If[EvenQ[#], #/2, # + Set[q, NextPrime[q]]] &, n, # > 1 &]], {n, 2^14}]][[-1, 1]], n] (* Michael De Vlieger, Sep 16 2025 *)

Prog

(Python)
from sympy import nextprime
from itertools import count, islice
def sisyphus(start): # generator of Sisyphus sequence beginning at start
    an, p = start, 1
    while True: yield an; an = an+(p:=nextprime(p)) if an&1 else an>>1
def b(n): # A388038
    return next(k for k, t in enumerate(sisyphus(n)) if t == 1)
def agen(): # generator of terms
    record = -1
    for k in count(1):
        if (v:=b(k)) > record: yield k; record = v
print(list(islice(agen(), 16))) # Michael S. Branicky, Sep 16 2025

Crossrefs

Cf. A388038, A388262 (records).

Sequence in context: A384154 A251703 A057755 * A262482 A293323 A257113

Adjacent sequences: A388260 A388261 A388262 * A388264 A388265 A388266

Keyword

nonn,hard,more

Author

Michael S. Branicky and James C. McMahon, Sep 16 2025

Extensions

a(27)-a(31) from Michael S. Branicky, Sep 23 2025

Status

approved