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A347668
Indices of records in A347409.
3
1, 2, 3, 15, 21, 75, 151, 1365, 5461, 7407, 14563, 87381, 184111, 932067, 5592405, 13256071, 26512143, 357913941, 1431655765, 3817748707, 22906492245, 91625968981, 244335917283, 1466015503701, 5212499568715, 10424999137431, 93824992236885
OFFSET
1,2
COMMENTS
Conjecture 1: A347409(a(n)) is even for n >= 11. Conjecture 2: all even numbers > 2 appear as A347409(a(n)) for some n. - Chai Wah Wu, Sep 29 2021
If conjectures 1 and 2 are true, then A347409(a(n)) = 2n - 6 for n >= 11, and hence a(n) <= (4^(n-3)-1)/3 for n >= 11 since A347409((4^(n-3)-1)/3) = 2n - 6. - Charles R Greathouse IV, Oct 25 2022
MATHEMATICA
A347409[n_]:=(c=n; sm=0; While[c>1, If[OddQ[c], c=3c+1, If[(s=IntegerExponent[c, 2])>sm, sm=s]; c/=2^s]]; sm)
upto=100000; a={}; rec=-1; Do[If[(r=A347409[i])>rec, rec=r; AppendTo[a, i]], {i, upto}]; a
PROG
(PARI) f(n)=my(nb=0); while (n != 1, if (n % 2, n=3*n+1, my(x = valuation(n, 2)); n /= 2^x; nb = max(nb, x)); ); nb; \\ A347409
lista(nn) = my(r=-1, m); for (n=1, nn, if ((m=f(n)) > r, print1(n, ", "); r = m); ); \\ Michel Marcus, Sep 10 2021
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Paolo Xausa, Sep 10 2021
EXTENSIONS
a(15) from Michel Marcus, Sep 10 2021
a(16)-a(17) from Alois P. Heinz, Sep 10 2021
a(18)-a(20) from Michael S. Branicky, Sep 28 2021
a(21)-a(22) from Michael S. Branicky, Sep 30 2021
a(23) from Michael S. Branicky, Oct 04 2021
a(24)-a(27) from Kevin P. Thompson, Apr 14 2022
STATUS
approved