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A347668 Indices of records in A347409.

%I A347668 #48 Oct 25 2022 07:34:22
%S A347668 1,2,3,15,21,75,151,1365,5461,7407,14563,87381,184111,932067,5592405,
%T A347668 13256071,26512143,357913941,1431655765,3817748707,22906492245,
%U A347668 91625968981,244335917283,1466015503701,5212499568715,10424999137431,93824992236885
%N A347668 Indices of records in A347409.
%C A347668 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
%C A347668 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
%H A347668 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%t A347668 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)
%t A347668 upto=100000;a={};rec=-1;Do[If[(r=A347409[i])>rec,rec=r;AppendTo[a,i]],{i,upto}];a
%o A347668 (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
%o A347668 lista(nn) = my(r=-1, m); for (n=1, nn, if ((m=f(n)) > r, print1(n, ", "); r = m);); \\ _Michel Marcus_, Sep 10 2021
%Y A347668 Cf. A006370, A070165, A135282, A347409, A347669, A002450.
%K A347668 nonn,hard,more
%O A347668 1,2
%A A347668 _Paolo Xausa_, Sep 10 2021
%E A347668 a(15) from _Michel Marcus_, Sep 10 2021
%E A347668 a(16)-a(17) from _Alois P. Heinz_, Sep 10 2021
%E A347668 a(18)-a(20) from _Michael S. Branicky_, Sep 28 2021
%E A347668 a(21)-a(22) from _Michael S. Branicky_, Sep 30 2021
%E A347668 a(23) from _Michael S. Branicky_, Oct 04 2021
%E A347668 a(24)-a(27) from _Kevin P. Thompson_, Apr 14 2022