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A352890
Number of iterations of map x -> A341515(x) needed to reach x <= 2 when starting from x=n, or -1 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).
5
0, 0, 1, 7, 2, 5, 3, 16, 8, 19, 4, 14, 5, 12, 6, 17, 6, 9, 7, 20, 20, 26, 8, 15, 9, 27, 17, 13, 9, 7, 10, 106, 13, 121, 7, 111, 11, 122, 27, 34, 12, 21, 13, 27, 15, 35, 14, 104, 10, 23, 28, 28, 15, 18, 21, 102, 122, 36, 16, 29, 17, 156, 21, 107, 14, 14, 18, 122, 123, 109, 19, 112, 20, 113, 10, 123, 8, 28, 21, 35
OFFSET
1,4
COMMENTS
The unbroken ray in the scatter plot corresponds to primes.
FORMULA
If n <= 2, a(n) = 0, otherwise a(n) = 1 + a(A341515(n)).
For n > 1, a(n) = A006577(A156552(n)).
For n >= 1, a(A000040(n)) = n-1.
For n >= 1, a(n) >= A352891(n).
For n >= 1, a(n) >= A352893(n).
PROG
(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A329603(n) = A005940(2+(3*A156552(n)));
A341515(n) = if(n%2, A064989(n), A329603(n));
A352890(n) = { my(k=0); while(n>2, n = A341515(n); k++); (k); };
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Apr 08 2022
STATUS
approved