A352897 Maximum value of bigomega (A001222) computed for all the terms x (including the starting term x=n), when map x -> A352892(x) is iterated 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).
0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 3, 1, 4, 3, 4, 1, 4, 2, 3, 3, 4, 1, 3, 1, 8, 3, 8, 2, 8, 1, 8, 4, 5, 1, 3, 1, 4, 3, 6, 1, 8, 2, 4, 3, 4, 1, 4, 3, 8, 8, 5, 1, 4, 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, 4, 3, 6, 5, 8, 3, 8, 1, 3, 4, 4, 1, 3, 1, 8, 3
Offset: 1
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Programs
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PARI
A352897(n) = { my(m=bigomega(n)); while(n>2, m = max(m,bigomega(n)); n = A352892(n)); (m); }; \\ Uses the code from A352892.
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PARI
A352897(n) = { my(m=bigomega(n)); while(n>2, m = max(m,bigomega(n)); n = A341515(n)); (m); }; \\ Slightly slower.
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PARI
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 }; A333860(n) = { my(mw=1); while(n>1, mw = max(hammingweight(n),mw); n = A139391(n)); (mw); }; A352897(n) = if(1==n,0,A333860(A156552(n)));
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