A347669 Indices of first occurrences of n in A347409.
1, 2, 4, 8, 3, 15, 21, 128, 75, 512, 151, 2048, 1365, 8192, 5461, 7407, 14563, 131072, 87381, 524288, 184111, 2097152, 932067, 6213783, 5592405, 33554432, 13256071, 134217728, 26512143, 530242875, 357913941, 1899273247, 1431655765, 8589934592, 3817748707, 34359738368
Offset: 0
Examples
a(5) = 15 because 5 occurs for the first time at position 15 in A347409.
Programs
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Mathematica
A347409[n_]:=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) nterms=20;Table[i=0;While[A347409[++i]!=n];i,{n,0,nterms-1}]
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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 a(n) = my(k=1); while (f(k) != n, k++); k; \\ Michel Marcus, Sep 10 2021
Extensions
a(21)-a(22) from Michel Marcus, Sep 10 2021
a(23)-a(28) from Alois P. Heinz, Sep 11 2021
a(29)-a(34) from Michael S. Branicky, Sep 28 2021
a(35) from Chai Wah Wu, Oct 02 2021