A063041 -id:A063041 - cp's OEIS frontend

A063042 Collatz-2 (A063041) trajectory starting at 3.

3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9

Offset: 0

Reinhard Zumkeller, Jul 07 2001

a(0) = a(5) = 3

A063041.

NestList[If[PrimeQ[#],#*Prime[PrimePi[#]-1]+1,#/Min@@First/@FactorInteger[#]]&,3,104] (* Jayanta Basu, May 27 2013 *)

a(0) = 3 and a(n) = A063041(a(n-1)) for n > 0

A063044 Collatz-2 (A063041) trajectory starting at 29.

Original entry on oeis.org

29, 668, 334, 167, 27222, 13611, 4537, 349, 121104, 60552, 30276, 15138, 7569, 2523, 841, 29, 668, 334, 167, 27222, 13611, 4537, 349, 121104, 60552, 30276, 15138, 7569, 2523, 841, 29, 668, 334, 167, 27222, 13611, 4537, 349, 121104, 60552, 30276, 15138, 7569

Offset: 0

Reinhard Zumkeller, Jul 07 2001

a(15) = 29 = a(0); this cycle occurs less frequently than A063042 (for the first few n); other nontrivial 29-cycle in trajectory starting at 167.

A063041, A063042.

a(0) = 29 and a(n) = A063041(a(n-1)) for n > 0

More terms from Sean A. Irvine, Apr 16 2023

A063043 Collatz-2 (A063041) trajectory starting at 17.

Original entry on oeis.org

17, 222, 111, 37, 1148, 574, 287, 41, 1518, 759, 253, 23, 438, 219, 73, 5184, 2592, 1296, 648, 324, 162, 81, 27, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36, 18, 9, 3, 7, 36

Offset: 0

Reinhard Zumkeller, Jul 07 2001

a(23) = a(28) = 9 and a(i) = a(j) <==> i = j for i, j < 28; same cycle values as A063042 but the conjecture that this is the only cycle for all starting values is not true: see A063044

Cf. A063041, A063042, A063044.

NestList[If[PrimeQ[#],#*Prime[PrimePi[#]-1]+1,#/Min@@First/@FactorInteger[#]]&,17,30] (* Jayanta Basu, May 27 2013 *)

a(0) = 17 and a(n) = A063041(a(n-1)) for n > 0

More terms from Sean A. Irvine, Apr 16 2023

A280707 Collatz-2 (A063041) trajectory starting at 47.

Original entry on oeis.org

47, 2022, 1011, 337, 111548, 55774, 27887, 353, 123198, 61599, 20533, 421357694, 210678847, 44385566460664754, 22192783230332377, 1707137171564029, 165918667661, 27529004277737692540278, 13764502138868846270139, 4588167379622948756713, 352935952278688365901, 3237944516318241889, 1577861856421, 2489648037916767181800822

Offset: 0

Antti Karttunen, Jan 23 2017

nonn

Will this sequence ever settle into a finite cycle?

Sean A. Irvine, Table of n, a(n) for n = 0..134 (terms 0..41 from Antti Karttunen, terms 42..103 from Hans Havermann)

Cf. A032742, A063041, A063045, A063046.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A063041(n) = if(2==n,3,if(isprime(n),1+(precprime(n-1)*n),A032742(n)));
n = 0; k = 47; while(n <= 41, write("b280707.txt", n, " ", k); k = A063041(k); n = n+1);

a(0) = 47 and for n > 1, a(n) = A063041(a(n-1)).

A063045 Largest value in Collatz-2 (A063041) trajectory starting at n.

Original entry on oeis.org

36, 36, 36, 36, 36, 36, 36, 36, 36, 144, 36, 144, 36, 36, 36, 5184, 36, 324, 36, 36, 144, 5184, 36, 36, 144, 36, 36, 121104, 36, 900, 36, 144, 5184, 36, 36, 5184, 324, 144, 40, 5184, 42, 1764, 144, 45, 5184

Offset: 2

Reinhard Zumkeller, Jul 07 2001

a(47) currently unknown but large (see A280707). - Sean A. Irvine, Apr 16 2023

			a(3) = 36 (see A063042), a(17) = 5184 (see A063043), a(29) = 121104 (see A063044)

Cf. A063041, A063042, A063043, A063044, A025586, A280707.

a(40), a(42) and a(45) corrected by Sean A. Irvine, Apr 16 2023

A063046 Length of non-periodic head in Collatz-2 (A063041) trajectory starting at n.

Original entry on oeis.org

6, 5, 7, 10, 6, 5, 8, 5, 11, 11, 7, 8, 6, 11, 9, 28, 5, 10, 12, 6, 12, 17, 8, 11, 9, 6, 7, 15, 12, 16, 10, 12, 29, 6, 5, 25, 11, 9, 13, 21, 7, 11, 13, 12, 18

Offset: 2

Reinhard Zumkeller, Jul 07 2001

			a(3) = 5 (see A063042), a(17) = 28 (see A063043), a(29) = 15 (see A063044)

Cf. A063041, A063042, A063043, A063044.

a(14) corrected by Sean A. Irvine, Apr 16 2023

cp's OEIS Frontend

A063042 Collatz-2 (A063041) trajectory starting at 3.

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A063044 Collatz-2 (A063041) trajectory starting at 29.

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A063043 Collatz-2 (A063041) trajectory starting at 17.

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A280707 Collatz-2 (A063041) trajectory starting at 47.

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A063045 Largest value in Collatz-2 (A063041) trajectory starting at n.

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A063046 Length of non-periodic head in Collatz-2 (A063041) trajectory starting at n.

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