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 A341516 The Collatz or 3x+1 function T (A014682) conjugated by unary-binary-encoding (A156552). 3
 1, 3, 2, 6, 3, 7, 5, 12, 4, 27, 7, 14, 11, 75, 6, 24, 13, 35, 17, 54, 10, 147, 19, 28, 9, 363, 8, 150, 23, 13, 29, 48, 14, 507, 15, 70, 31, 867, 22, 108, 37, 343, 41, 294, 12, 1083, 43, 56, 25, 63, 26, 726, 47, 175, 21, 300, 34, 1587, 53, 26, 59, 2523, 20, 96, 33, 847, 61, 1014, 38, 243, 67, 140, 71, 2883, 18, 1734 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Collatz-conjecture can be formulated via this sequence by postulating that all iterations of a(n), starting from any n > 1, will eventually end reach the cycle [2, 3]. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA If n is odd, then a(n) = A064989(n), otherwise a(n) = A064989(A329603(n)). a(n) = A005940(1+A014682(A156552(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), 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))); A341516(n) = if(n%2, A064989(n), A064989(A329603(n))); CROSSREFS Cf. A005940, A014682, A064989, A156552, A329603. Cf. A341515 for a variant. Sequence in context: A038572 A334667 A245676 * A060992 A064455 A141619 Adjacent sequences:  A341513 A341514 A341515 * A341517 A341518 A341519 KEYWORD nonn AUTHOR Antti Karttunen, Feb 15 2021 STATUS approved

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Last modified August 4 08:57 EDT 2021. Contains 346445 sequences. (Running on oeis4.)