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A352896
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Maximum value of bigomega (A001222) computed for the terms x after the initial n, when map x -> A352892(x) is iterated starting from x=n down to the first x <= 2, or -1 if such number is never reached. Here A352892 is the next odd term in the Collatz or 3x+1 map (A139391) conjugated by unary-binary-encoding (A156552).
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6
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0, 1, 1, 2, 1, 1, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 2, 1, 4, 3, 4, 1, 4, 2, 3, 3, 4, 1, 1, 1, 8, 3, 8, 2, 8, 1, 8, 4, 5, 1, 3, 1, 4, 3, 6, 1, 8, 2, 4, 3, 4, 1, 3, 3, 8, 8, 5, 1, 3, 1, 8, 4, 8, 3, 3, 1, 8, 8, 8, 1, 8, 1, 8, 3, 8, 2, 4, 1, 6, 4, 7, 1, 4, 4, 7, 6, 5, 1, 3, 3, 6, 5, 8, 3, 8, 1, 3, 4, 4, 1, 3, 1, 8, 3
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OFFSET
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1,4
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COMMENTS
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Equally, maximum value of bigomega (A001222) computed for the terms x after the initial n, when map x -> A341515(x) is iterated starting from x=n.
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LINKS
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FORMULA
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PROG
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(PARI) A352896(n) = if(n<=2, n-1, my(m=0); while(n>2, n = A352892(n); m = max(m, bigomega(n))); (m)); \\ Needs also code from A352892.
(PARI) A352896(n) = if(n<=2, n-1, my(m=0); while(n>2, n = A341515(n); m = max(m, bigomega(n))); (m)); \\ Slower, but equivalent.
(PARI)
\\ Faster:
A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391
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 };
A352895(n) = { my(mw=1); while(n>1, n = A139391(n); mw = max(hammingweight(n), mw)); (mw); };
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CROSSREFS
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Cf. A000040, A001222, A005940, A064989, A156552, A329603, A341515, A352892, A352895, A352897, A352899.
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KEYWORD
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AUTHOR
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STATUS
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approved
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