A050012 -id:A050012 - cp's OEIS frontend

A050013 a(n) = position of n in A050012.

1, 7, 3, 21, 6, 13, 2, 39, 20, 5, 126, 12, 179, 8, 194, 38, 171, 19, 110, 205, 4, 125, 220, 11, 102, 178, 273, 22, 117, 193, 269, 37, 94, 170, 208, 18, 33, 109, 166, 204, 261, 14, 67, 124, 162, 219, 257, 295, 10, 101, 139, 177, 215, 272, 291, 40, 78, 116, 154

Offset: 1

Clark Kimberling

Cf. A050012.

A050014 Numbers k such that A050012(k) < A050012(k+1).

Original entry on oeis.org

1, 3, 7, 8, 13, 14, 21, 22, 23, 28, 33, 39, 40, 41, 42, 51, 55, 58, 61, 67, 68, 72, 78, 81, 84, 88, 94, 95, 102, 104, 110, 111, 117, 118, 126, 127, 131, 134, 139, 142, 145, 149, 154, 157, 162, 166, 171, 172, 179, 180, 184, 188, 194

Offset: 1

Clark Kimberling

A050015 Numbers k such that b(k) > b(k+1), where b=A050012.

Original entry on oeis.org

2, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 38, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 59, 60, 62, 63, 64, 65, 66, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 82, 83, 85, 86

Offset: 1

Clark Kimberling

A050000 a(n) = floor(a(n-1)/2) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 3*a(n-1).

Original entry on oeis.org

1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, 21, 10, 5, 15, 45, 22, 11, 33, 16, 8, 24, 12, 36, 108, 324, 162, 81, 40, 20, 60, 30, 90, 270, 135, 67, 201, 100, 50, 25, 75, 37, 111, 55, 165, 82, 41, 123, 61, 183, 91, 273, 136, 68

Offset: 1

Clark Kimberling

This permutation of the natural numbers is the multiply-and-divide (MD) sequence for (M,D)=(3,2). The "MD question" is this: for relatively prime M and D, does the MD sequence contain every positive integer exactly once? An affirmative proof for the more general condition that log base D of M is irrational is given by Mateusz Kwaśnicki in Crux Mathematicorum 30 (2004) 235-239. - Clark Kimberling, Jun 30 2004

T. D. Noe, Table of n, a(n) for n = 1..10000
Clark Kimberling, Unsolved Problems and Rewards.
Mateusz Kwaśnicki, The solution of M-D problem (2008).
Index entries for sequences that are permutations of the natural numbers

Cf. A050076, A050001 (inverse).
MD sequences:
A050076 (2,3), A050124 (2,5),
this sequence (3,2), A050104 (3,4),
A050080 (4,3),
A050004 (5,2), A050084 (5,3), A050108 (5,4),
A050008 (6,2), A050088 (6,3), A050112 (6,4),
A050012 (7,2), A050092 (7,3),
A050096 (8,3),
A050016 (9,2),
A050020 (10,2), A050100 (10,3).

a050000 n = a050000_list !! (n-1)
a050000_list = 1 : f [1,0] where
   f xs'@(x:xs) | x `div` 2 `elem` xs = 3 * x : f (3 * x : xs')
                | otherwise = x `div` 2 : f (x `div` 2 : xs')
-- Reinhard Zumkeller, Nov 13 2011

a[0] = 0; a[1] = 1; a[n_] := a[n] = (b = Floor[a[n-1]/2]; If[FreeQ[Table[ a[k], {k, 0, n-2}], b], b, 3*a[n-1]]);
Array[a, 60] (* Jean-François Alcover, Jul 13 2016 *)

A090300 a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.

Original entry on oeis.org

2, 14, 198, 2786, 39202, 551614, 7761798, 109216786, 1536796802, 21624372014, 304278004998, 4281516441986, 60245508192802, 847718631141214, 11928306344169798, 167844007449518386, 2361744410637427202

Offset: 0

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004

a(n+1)/a(n) converges to (7+sqrt(50)) = 14.071067811...
Lim_{n->infinity} a(n)/a(n+1) = 0.071067811... = 1/(7+sqrt(50)) = sqrt(50) - 7.
Lim_{n->infinity} a(n+1)/a(n) = 14.071067811... = (7+sqrt(50)) = 1/(sqrt(50) - 7).

			a(4) = 39202 = 14*a(3) + a(2) = 14*2786 + 198 = (7+sqrt(50))^4 + (7-sqrt(50))^4 = 39201.999974491 + 0.000025508 = 39202.

Harvey P. Dale, Table of n, a(n) for n = 0..870
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
Index entries for linear recurrences with constant coefficients, signature (14, 1).

Cf. A050012.

LinearRecurrence[{14,1},{2,14},20] (* Harvey P. Dale, Jul 12 2020 *)

a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
a(n) = (7+sqrt(50))^n + (7-sqrt(50))^n.
(a(n))^2 = a(2n)-2 if n = 1, 3, 5, ...; (a(n))^2 = a(2n)+2 if n = 2, 4, 6, ....
G.f.: (2-14*x)/(1-14*x-x^2). - Philippe Deléham, Nov 02 2008

More terms from Ray Chandler, Feb 14 2004

cp's OEIS Frontend

A050013 a(n) = position of n in A050012.

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A050014 Numbers k such that A050012(k) < A050012(k+1).

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A050015 Numbers k such that b(k) > b(k+1), where b=A050012.

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A050000 a(n) = floor(a(n-1)/2) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 3*a(n-1).

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A090300 a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.

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