cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A112978 Inverse of A112975.

Original entry on oeis.org

1, 2, 3, 5, 12, 4, 17, 6, 7, 8, 27, 9, 33, 10, 11, 13, 43, 14, 49, 15, 16, 18, 59, 19, 20, 21, 22, 23, 74, 24, 80, 25, 26, 28, 29, 30, 94, 31, 32, 34, 106, 35, 112, 36, 37, 38, 122, 39, 40, 41, 42, 44, 138, 45, 46, 47, 48, 50, 154, 51, 159, 52, 53, 54, 55, 56, 174, 57, 58, 60
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 08 2005

Keywords

Comments

A112979 = a(a(n));
a(n) = A112975(A112979(n)) = A112979(A112975(n)).

Links

Crossrefs

Cf. A112990.

A112976 Position of n-th prime in A112975.

Original entry on oeis.org

2, 3, 12, 17, 27, 33, 43, 49, 59, 74, 80, 94, 106, 112, 122, 138, 154, 159, 174, 186, 193, 208, 219, 235, 255, 267, 273, 283, 290, 301, 337, 348, 364, 371, 396, 402, 417, 434, 445, 462, 479, 485, 511, 517, 529, 535, 565, 596, 607, 613, 625, 642, 648
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 08 2005

Keywords

Comments

A112975(a(n)) = A000040(n).

Crossrefs

Cf. A112988.

A112977 A112975(A112975(n)).

Original entry on oeis.org

1, 2, 3, 8, 6, 10, 12, 14, 5, 18, 20, 4, 21, 22, 25, 26, 9, 27, 30, 32, 33, 11, 34, 36, 39, 13, 15, 40, 42, 44, 46, 48, 16, 49, 51, 52, 54, 55, 57, 19, 58, 60, 7, 62, 64, 65, 66, 68, 24, 69, 70, 74, 75, 76, 77, 78, 81, 82, 28, 84, 86, 29, 88, 90, 91, 92, 31, 94, 95, 98, 99, 100, 102
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 08 2005

Keywords

Comments

Inverse integer permutation of A112979;
A112978(a(n)) = a(A112978(n)) = A112975(n).

Links

A089088 a(0) = 1, a(1) = 2; for n > 1, a(n) = smallest positive number not already in sequence which has GCD > 1 with some earlier term.

Original entry on oeis.org

1, 2, 4, 6, 3, 8, 9, 10, 5, 12, 14, 7, 15, 16, 18, 20, 21, 22, 11, 24, 25, 26, 13, 27, 28, 30, 32, 33, 34, 17, 35, 36, 38, 19, 39, 40, 42, 44, 45, 46, 23, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 29, 60, 62, 31, 63, 64, 65, 66, 68, 69, 70, 72, 74, 37, 75, 76, 77, 78, 80, 81, 82, 41, 84, 85, 86, 43, 87, 88, 90, 91, 92, 93, 94, 47, 95, 96, 98, 99
Offset: 0

Views

Author

Leroy Quet, Dec 04 2003

Keywords

Comments

This is a permutation of the natural numbers.
For n > 2: a(n) is prime iff a(n) < a(n-1); a(A112988(n)) = A000040(n); inverse: A112990. - Reinhard Zumkeller, Oct 08 2005
For n > 3, a(n) can be described as follows: all composite numbers in natural order, with primes inserted so that every prime p immediately follows 2p. - Ivan Neretin, Apr 26 2015

Links

Crossrefs

Cf. A064413.
Cf. A112975.

Programs

  • Haskell
    import Data.List (delete)
a089088 n = a089088_list !! n
a089088_list = 1 : 2 : f [3..] [1,2] where
  f xs ys = y : f (delete y xs) (y : ys) where
    y = head $ filter (\z -> any (> 1) $ map (gcd z) ys) xs
-- Reinhard Zumkeller, Feb 27 2013
  • Mathematica
    A089088 = {a[0] = 1, a[1] = 2}; a[n_] := Catch[For[k = Min[ Complement[ Range[Max[A089088] + 1], A089088]], True, k++, If[ !MemberQ[A089088, k] && Or @@ (GCD[k, #] > 1&) /@ A089088, AppendTo[A089088, k]; Throw[k]]]]; Table[a[n], {n, 0, 88}] (* Jean-François Alcover, Jul 18 2012 *)
Nest[Append[#1, Block[{k = 1}, While[Nand[FreeQ[#1, k], AnyTrue[#1, ! CoprimeQ[#, k] &]], k++]; k]] &, {1, 2}, 87] (* Michael De Vlieger, Nov 18 2017 *)

Extensions

More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Jun 16 2004

A112979 A112978(A112978(n)).

Original entry on oeis.org

1, 2, 3, 12, 9, 5, 43, 4, 17, 6, 22, 7, 26, 8, 27, 33, 112, 10, 40, 11, 13, 14, 154, 49, 15, 16, 18, 59, 62, 19, 67, 20, 21, 23, 74, 24, 81, 80, 25, 28, 90, 29, 95, 30, 94, 31, 104, 32, 34, 106, 35, 36, 119, 37, 38, 122, 39, 41, 133, 42, 137, 44, 138, 45, 46, 47, 150, 48, 50, 51
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 08 2005

Keywords

Comments

Inverse integer permutation of A112977;
A112975(a(n)) = a(A112975(n)) = A112978(n).

Links

Showing 1-5 of 5 results.

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