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 1-4 of 4 results.

A065307 "Inverse" to A065306.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 11, 12, 13, 15, 14, 16, 17, 18, 19, 24, 20, 21, 25, 22, 26, 29, 23, 27, 28, 33, 30, 31, 34, 35, 32, 41, 36, 38, 37, 39, 40, 42, 43, 51, 44, 45, 52, 46, 48, 53, 47, 54, 58, 49, 55, 67, 50, 56, 57, 62, 59, 60, 63, 64, 61, 74, 65, 68, 66, 69, 70, 79
Offset: 1

Views

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 29 2001

Keywords

Links

Crossrefs

Cf. A065305, A065306.
Cf. A205666 (fixed points).

Programs

  • Haskell
    import Data.List (elemIndex)
import Data.Maybe (fromJust)
a065307 n = (fromJust $ elemIndex n a065306_list) + 1
-- Reinhard Zumkeller, Jan 30 2012

A205666 Fixed points of permutations A065306 and A065307.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 19, 38, 42, 43, 55, 63, 64, 68, 75, 76, 86, 106, 107, 108, 109, 112, 113, 120, 131, 156, 157, 175, 185, 194, 233, 270, 301, 369, 380, 438, 443, 470, 531, 663, 760, 803, 810, 847, 871, 934, 999, 1021, 1044
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 30 2012

Keywords

Comments

A065306(a(n)) = a(n); A065307(a(n)) = a(n).

Links

Programs

  • Haskell
    a205666 n = a205666_list !! (n-1)
a205666_list = [x | x <- [1..], a065306 x == fromIntegral x]
-- Reinhard Zumkeller, Jan 30 2012

A065305 Triangular array giving means of two odd primes: T(n,k) = (n-th prime + k-th prime)/2, n >= k >= 2.

Original entry on oeis.org

3, 4, 5, 5, 6, 7, 7, 8, 9, 11, 8, 9, 10, 12, 13, 10, 11, 12, 14, 15, 17, 11, 12, 13, 15, 16, 18, 19, 13, 14, 15, 17, 18, 20, 21, 23, 16, 17, 18, 20, 21, 23, 24, 26, 29, 17, 18, 19, 21, 22, 24, 25, 27, 30, 31, 20, 21, 22, 24, 25, 27, 28, 30, 33, 34, 37, 22, 23, 24, 26, 27, 29, 30
Offset: 2

Views

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 29 2001

Keywords

Examples

			3; 4,5; 5,6,7; 7,8,9,11; ...

Links

Crossrefs

Cf. A065306.
a(n, k) = A065342(n, k)/2 [but note different offsets]
Cf. A098090 (left edge), A065091 (right edge), A000040.

Programs

  • Haskell
    import Data.List (inits)
a065305 n k = a065305_tabl !! (n-2) !! (k - 1)
a065305_row n = a065305_tabl !! (n-2)
a065305_tabl = zipWith (map . (flip div 2 .) . (+))
                       a065091_list $ tail $ inits a065091_list
-- Reinhard Zumkeller, Aug 02 2015, Jan 30 2012
  • Maple
    seq(seq((ithprime(i)+ithprime(j))/2,j=2..i),i=2..20)

A187098 A permutation of the natural numbers related to Goldbach conjecture.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 8, 11, 10, 13, 14, 12, 15, 17, 18, 16, 19, 21, 20, 23, 24, 25, 22, 27, 26, 29, 30, 28, 31, 33, 32, 35, 36, 39, 38, 42, 37, 34, 40, 43, 45, 41, 44, 48, 49, 46, 51, 47, 50, 53, 56, 57, 52, 55, 54, 60, 58, 63, 59, 65, 62, 66, 61, 70, 67, 69, 68, 71, 72, 73, 75, 74, 77, 78, 76, 81, 80, 84
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 04 2011

Keywords

Comments

a(n) = if n <= 2 then n else A187085(n-2)/2;
for n > 2: a(n+1) = a(n) + (A187072(n) - A187072(n-2)) / 2.

Links

Crossrefs

Cf. A065306, A187099 (inverse).
Cf. A187085, A187072.

Programs

  • Haskell
    a187098 n = a187098_list !! (n-1)
a187098_list = 1 : 2 : map (`div` 2) a187085_list
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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