A239965 -id:A239965 - cp's OEIS frontend

A238862 Inverse permutation to A239965.

1, 2, 3, 4, 6, 7, 5, 9, 11, 8, 10, 12, 14, 15, 13, 18, 20, 16, 24, 19, 17, 21, 23, 25, 22, 27, 29, 26, 28, 30, 32, 33, 31, 35, 37, 38, 36, 41, 43, 39, 47, 51, 34, 40, 42, 44, 46, 48, 45, 50, 52, 49, 53, 55, 57, 54, 58, 60, 61, 56, 65, 63, 66, 59, 64, 69, 72

Offset: 1

Reinhard Zumkeller, Apr 30 2014

nonn

a(A239965(n)) = A239965(a(n)) = n;

A018252(a(n)) = A240024(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A239943 (fixed points).

import Data.List (elemIndex); import Data.Maybe (fromJust)
a238862 = (+ 1) . fromJust . (`elemIndex` a239965_list)

A239943 Fixed points of the permutations A239965 and A238862.

Original entry on oeis.org

1, 2, 3, 4, 12, 23, 30, 48, 50, 53, 68, 79, 80, 81, 92, 104, 105, 110, 112, 122, 131, 138, 149, 153, 160, 180, 185, 191, 201, 208, 216, 223, 242, 265, 279, 292, 308, 310, 317, 332, 337, 344, 348, 351, 362, 374, 381, 401, 410, 416, 431, 436, 446, 451, 454

Offset: 1

Reinhard Zumkeller, Apr 30 2014

nonn

a(n) = A239965(a(n)) = A238862(a(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

a239943 n = a239943_list !! (n-1)
a239943_list = [x | x <- [1..], a239965 x == x]

A240024 Nonprime EKG sequence, cf. A064413: a(1) = 1, a(2) = 4 and for n > 2, a(n) = smallest composite number not already used which shares a factor with a(n-1).

Original entry on oeis.org

1, 4, 6, 8, 10, 12, 9, 15, 18, 14, 16, 20, 22, 24, 21, 27, 30, 25, 35, 28, 26, 32, 34, 36, 33, 39, 42, 38, 40, 44, 46, 48, 45, 50, 52, 54, 51, 57, 60, 55, 65, 70, 49, 56, 58, 62, 64, 66, 63, 69, 72, 68, 74, 76, 78, 75, 80, 82, 84, 77, 88, 86, 90, 81, 87, 93

Offset: 1

Reinhard Zumkeller, Apr 30 2014

nonn

A239965 gives the position of the n-th nonprime; a(A239965(n))=A018252(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, EKG Sequence
Index entries for sequences related to EKG sequence

Cf. A064413, A064664 (EKG sequence).

Cf. A018252, A075570, A239965.

import Data.List (delete, genericIndex)
a240024 n = genericIndex a240024_list (n - 1)
a240024_list = 1 : ekg 4 a002808_list where
   ekg x zs = f zs where
       f (y:ys) = if gcd x y > 1 then y : ekg y (delete y zs) else f ys

a = {1, 4}; Do[k = 6; While[Or[PrimeQ@ k, MemberQ[a, k], CoprimeQ[a[[i - 1]], k]], k++]; AppendTo[a, k], {i, 3, 66}]; a (* Michael De Vlieger, Sep 01 2016 *)

cp's OEIS Frontend

A238862 Inverse permutation to A239965.

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A239943 Fixed points of the permutations A239965 and A238862.

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A240024 Nonprime EKG sequence, cf. A064413: a(1) = 1, a(2) = 4 and for n > 2, a(n) = smallest composite number not already used which shares a factor with a(n-1).

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