A180078 -id:A180078 - cp's OEIS frontend

A180076 a(n+1) = if it exists, smallest number not occurring earlier that is contained in binary representation of a(n), otherwise: a(n+1) = 3*a(n)+1; a(0) = 0.

0, 1, 4, 2, 7, 3, 10, 5, 16, 8, 25, 6, 19, 9, 28, 12, 37, 18, 55, 11, 34, 17, 52, 13, 40, 20, 61, 14, 43, 21, 64, 32, 97, 24, 73, 36, 109, 22, 67, 33, 100, 50, 151, 23, 70, 35, 106, 26, 79, 15, 46, 139, 69, 208, 80, 241, 30, 91, 27, 82, 41, 124, 31, 94, 47, 142, 71, 214, 53, 160

Offset: 0

Reinhard Zumkeller, Aug 14 2010

Permutation of the natural numbers with inverse A180077;
if a(n-1) > a(n) then a(n) < a(n+1) = 3*a(n)+1;
see A180110 for m with a(m-2) < a(m-1) < a(m);
A180078(n) = a(a(n));
a(A180079(n)) = A180079(a(n)) = A180077(n);
A180080 and A180081 give record values and where they occur.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A007088, A016777.
Cf. A030308.
Cf. A062383.

import Data.List (delete)
a180076 n = a180076_list !! n
a180076_list :: [Integer]
a180076_list = 0 : f 0 [1..] where
   f x zs = y : f y (delete y zs) where
     y = if null ys then 3 * x + 1 else head ys
     ys = [y | y <- takeWhile (< x) zs, binInfix y x]
   binInfix u v = ib v where
     ib w = w `mod` m == u || w > u && ib (w `div` 2)
     m = a062383 u
-- Reinhard Zumkeller, Mar 13 2014, Feb 19 2013

A180077 Inverse permutation to A180076.

Original entry on oeis.org

0, 1, 3, 5, 2, 7, 11, 4, 9, 13, 6, 19, 15, 23, 27, 49, 8, 21, 17, 12, 25, 29, 37, 43, 33, 10, 47, 58, 14, 99, 56, 62, 31, 39, 20, 45, 35, 16, 93, 127, 24, 60, 106, 28, 75, 143, 50, 64, 71, 79, 41, 95, 22, 68, 129, 18, 164, 148, 120, 112, 141, 26, 110, 108, 30, 89, 77, 38, 91, 52

Offset: 0

Reinhard Zumkeller, Aug 14 2010

nonn

A180079(n) = a(a(n));

a(A180078(n)) = A180078(a(n)) = A180076(n).

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences that are permutations of the natural numbers

import Data.List (elemIndex); import Data.Maybe (fromJust)
a180077 = fromJust . (`elemIndex` a180076_list)
-- Reinhard Zumkeller, Mar 13 2014

A180079 A180077(A180077(n)).

Original entry on oeis.org

0, 1, 5, 7, 3, 4, 19, 2, 13, 23, 11, 12, 49, 43, 58, 79, 9, 29, 21, 15, 10, 99, 16, 28, 39, 6, 64, 120, 27, 104, 164, 110, 62, 127, 25, 143, 45, 8, 135, 107, 33, 141, 46, 14, 162, 85, 41, 30, 66, 48, 60, 83, 37, 91, 152, 17, 355, 80, 170, 331, 286, 47, 336, 190, 56, 114, 97

Offset: 0

Reinhard Zumkeller, Aug 14 2010

nonn

Permutation of the natural numbers with inverse A180078;

a(A180076(n)) = A180076(a(n)) = A180077(n).

Index entries for sequences that are permutations of the natural numbers

cp's OEIS Frontend

A180076 a(n+1) = if it exists, smallest number not occurring earlier that is contained in binary representation of a(n), otherwise: a(n+1) = 3*a(n)+1; a(0) = 0.

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Haskell

A180077 Inverse permutation to A180076.

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Haskell

A180079 A180077(A180077(n)).

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