A347668 Indices of records in A347409.

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

Author

Paolo Xausa, Sep 10 2021

Keywords

• nonn
• hard
• more

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

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A070165, A135282, A347409, A347669, A002450.

Programs

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

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

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