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 A224165 Number of cycles the reduced complex Collatz function using 3 + (2n-1)i takes to hit 1 + i, or 0 if this never happens. 1
 5, 5, 5, 13, 9, 5, 13, 5, 9, 5, 17, 9, 13, 13, 5, 9, 21, 9, 9, 17, 0, 5, 9, 5, 13, 13, 13, 13, 17, 5, 9, 9, 0, 9, 9, 13, 13, 5, 17, 17, 17, 17, 17, 17, 21, 9, 5, 5, 25, 13, 5, 0, 25, 13, 13, 17, 9, 5, 13, 9, 33, 9, 9, 0, 0, 21, 9, 33, 21, 9, 13, 5, 13, 9, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The complex Collatz function takes a complex number z to 3iz + (1+i). The resulting real part is divided by 2 until it's odd, and the same for the imaginary part. The effect here is that say 4 + 14i is reduced to 1 + 7i. The reduced complex Collatz function does all this in the same cycle. Equals 0 for n = 21, 33, 52, 64, 65, 81, 82, 101, 103, 127, 129, 130, 163, 201, 204, 206, 253, 254... This is conjectured to be infinite and the same as in A224067. For example, 3 + 41i yields -61 + 5i, -7 + -91i, 137 + -5i, 1 + 103i, -77 + 1i, -1 + -115i, 173 + -1i, 1 + 65i, -97 + 1i, -1 + -145i, 109 + -1i, 1 + 41i, -61 + 1i, -1 + -91i, 137 + -1i, 1 + 103i, -77 + 1i, -1 + -115i, 173 + -1i, 1 + 65i, -97 + 1i, -1 + -145i, 109 + -1i, 1 + 41i, which becomes cyclic about 1 + 41i. LINKS Table of n, a(n) for n=1..75. Eric Weisstein, Mathworld: Collatz Problem Wikipedia, Collatz Problem EXAMPLE a(5) = 13 because rcC(3 + 7i) yields -5 + 5i, -7 + -7i, 11 + -5i, 1 + 17i, -25 + 1i, -1 + -37i, 7 + -1i, 1 + 11i, -1 + 1i, -1 + -1i, 1 + -1i, 1 + 1i, which is 13 terms. PROG (JavaScript) for (b=1; b<150; b+=2) { c=1; r[0]=3; i[0]=b; while (r[c-1]!=1 || i[c-1]!=1 && c<1000) { i[c]=r[c-1]*3+1; r[c]=-i[c-1]*3+1; while (r[c]%2==0) r[c]/=2; while (i[c]%2==0) i[c]/=2; c++; } document.write(c+", "); } CROSSREFS Cf. A224067. Sequence in context: A262947 A265821 A266953 * A330318 A334934 A131286 Adjacent sequences: A224162 A224163 A224164 * A224166 A224167 A224168 KEYWORD nonn,less AUTHOR Jon Perry, Apr 02 2013 STATUS approved

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Last modified September 7 09:43 EDT 2024. Contains 375730 sequences. (Running on oeis4.)