A065649 -id:A065649 - cp's OEIS frontend

A065650 Inverse permutation to A065649.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 15, 17, 19, 21, 23, 25, 27, 29, 31, 12, 30, 37, 39, 41, 43, 45, 47, 49, 51, 13, 32, 50, 59, 61, 63, 65, 67, 69, 71, 14, 34, 52, 70, 81, 83, 85, 87, 89, 91, 16, 35, 54, 72, 90, 103, 105, 107, 109, 111, 18, 36, 56, 74, 92, 110, 125, 127

Offset: 0

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Nov 09 2001

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

Cf. A033307, A065648, A065649, A261334.

Cf. A261279 (fixed points), A261294.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a065650 = fromJust . (`elemIndex` a065649_list)
-- Reinhard Zumkeller, Aug 13 2015

Offset changed by Reinhard Zumkeller, Aug 13 2015

A261279 Fixed points of A065649, a permutation of nonnegative integers based on Champernowne's constant.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 32, 204, 354, 40964, 50322, 65964, 263125, 319166, 513764, 626082, 701753, 813764, 6179084, 6377296, 9679084, 72205374, 73333335, 74470716, 74522672, 87181372, 97270723, 112205374, 114522672, 517336266, 851684556, 1224783704

Offset: 1

Reinhard Zumkeller, Aug 14 2015

nonn

Also fixed points of A065650, A261293 and A261294.

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..2063

Cf. A065649, A065650, A261293, A261294, A261335.

a261279 n = a261279_list !! (n-1)
a261279_list = [x | x <- [0..], a065649 x == x]

a(23)-a(36) from Hiroaki Yamanouchi, Aug 21 2015

A261293 a(n) = A065649(A065649(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 20, 25, 21, 30, 31, 35, 41, 40, 12, 45, 51, 50, 13, 115, 61, 60, 14, 81, 71, 32, 165, 92, 43, 103, 16, 54, 91, 114, 17, 65, 101, 125, 18, 76, 111, 126, 19, 121, 22, 26, 70, 131, 87, 36, 141, 46, 42, 151, 52, 56, 62

Offset: 0

Reinhard Zumkeller, Aug 14 2015

nonn

Permutation of the nonnegatve integers with inverse A261294;

a(A065650(n)) = A065650(a(n)) = A065649(n).

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

Cf. A065649, A065650, A261294 (inverse), A261279 (fixed points).

Haskell
```
a261293 = a065649 . a065649
```

A261333 a(n) = 10*(A256100(n+1)-1) + A007376(n+1), a simple variation of A065649.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 0, 21, 31, 41, 12, 51, 13, 61, 14, 71, 15, 81, 16, 91, 17, 101, 18, 111, 19, 22, 10, 32, 121, 42, 52, 62, 23, 72, 24, 82, 25, 92, 26, 102, 27, 112, 28, 122, 29, 33, 20, 43, 131, 53, 132, 63, 73, 83, 34, 93, 35, 103, 36, 113, 37

Offset: 0

Reinhard Zumkeller, Aug 15 2015

Permutation of the nonnegatve integers with inverse A261334.

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

Cf. A256100, A007376, A261334 (inverse), A261335 (fixed points), A065649.

a261333 n = a261333_list !! n
a261333_list = zipWith (+)
               (map ((* 10) . subtract 1) a256100_list) a007376_list

A065648 a(0) = 1 and for n > 0: a(n) = number of indices 0 <= i <= n with A033307(i)=A033307(n), where A033307 is the sequence of decimal digits of Champernowne's constant 0.123456789101112131415...

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 2, 12, 2, 3, 3, 4, 13, 5, 6, 7, 3, 8, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 3, 4, 4, 5, 14, 6, 14, 7, 8, 9, 4, 10, 4, 11, 4, 12, 4, 13, 4, 14, 4, 5, 5, 6, 15, 7, 15, 8, 15, 9, 10, 11, 5, 12, 5, 13, 5, 14, 5, 15, 5, 6, 6

Offset: 0

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Nov 09 2001

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A033307, A065649, A065650.

Cf. A256100.

a065648 n = a065648_list !! n
a065648_list = f (0 : a033307_list) $ take 10 $ repeat 1 where
   f (d:ds) counts = y : f ds (xs ++ (y + 1) : ys) where
                           (xs, y:ys) = splitAt d counts
-- Reinhard Zumkeller, Aug 13 2015

Definition and offset adjusted to follow a later change of A033307. - Reinhard Zumkeller, Aug 13 2015

A261294 a(n) = A065650(A065650(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 25, 29, 12, 37, 41, 45, 49, 13, 15, 51, 65, 69, 14, 52, 81, 85, 89, 16, 17, 32, 91, 109, 18, 56, 92, 125, 129, 20, 19, 59, 35, 131, 22, 58, 96, 132, 169, 24, 23, 61, 72, 38, 171, 62, 100, 136, 172, 28, 27, 63, 103

Offset: 0

Reinhard Zumkeller, Aug 14 2015

Permutation of the nonnegatve integers with inverse A261293;

a(A065649(n)) = A065649(a(n)) = A065650(n).

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

Cf. A065650, A065649, A261293 (inverse), A261279 (fixed points).

Haskell
```
a261294 = a065650 . a065650
```

cp's OEIS Frontend

A065650 Inverse permutation to A065649.

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A261279 Fixed points of A065649, a permutation of nonnegative integers based on Champernowne's constant.

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A261293 a(n) = A065649(A065649(n)).

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A261333 a(n) = 10*(A256100(n+1)-1) + A007376(n+1), a simple variation of A065649.

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A065648 a(0) = 1 and for n > 0: a(n) = number of indices 0 <= i <= n with A033307(i)=A033307(n), where A033307 is the sequence of decimal digits of Champernowne's constant 0.123456789101112131415...

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A261294 a(n) = A065650(A065650(n)).

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Haskell