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 1-6 of 6 results.

A115408 Integer permutation induced by A024431.

Original entry on oeis.org

1, 6, 15, 3, 2, 5, 4, 28, 45, 10, 66, 9, 14, 91, 13, 8, 7, 120, 12, 11, 153, 190, 21, 231, 276, 20, 325, 378, 435, 496, 27, 561, 630, 26, 703, 19, 780, 18, 861, 946, 1035, 17, 16, 25, 1128, 24, 1225, 1326, 1431, 23, 22, 1540, 1653, 36, 1770, 1891, 2016, 2145
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 22 2006

Keywords

Comments

a(n) = A115406(n)*(A115406(n)-1)/2 + A115407(n) + 1;
inverse: A115409.

Links

Programs

  • Haskell
    import Data.List (elemIndex); import Data.Maybe (fromJust)
a115408 = (+ 1) . fromJust . (`elemIndex` a115409_list)
-- Reinhard Zumkeller, Sep 16 2014

A115406 Unique m such that A024431(m) - A024431(A115407(n)) = n.

Original entry on oeis.org

1, 3, 5, 2, 2, 3, 3, 7, 9, 4, 11, 4, 5, 13, 5, 4, 4, 15, 5, 5, 17, 19, 6, 21, 23, 6, 25, 27, 29, 31, 7, 33, 35, 7, 37, 6, 39, 6, 41, 43, 45, 6, 6, 7, 47, 7, 49
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 22 2006

Keywords

Comments

A024431(a(n)) - A024431(A115407(n)) = n.

Crossrefs

Cf. A115408.

A115407 Unique m such that A024431(A115406(n)) - A024431(m) = n.

Original entry on oeis.org

0, 2, 4, 1, 0, 1, 0, 6, 8, 3, 10, 2, 3, 12, 2, 1, 0, 14, 1, 0, 16, 18, 5, 20, 22, 4, 24, 26, 28, 30, 5, 32, 34, 4, 36, 3, 38, 2, 40, 42, 44, 1, 0, 3, 46, 2, 48
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 22 2006

Keywords

Comments

A024431(A115406(n)) - A024431(a(n)) = n.

Crossrefs

Cf. A115408.

A247414 First differences of A024431.

Original entry on oeis.org

1, 4, 2, 10, 3, 23, 8, 54, 9, 117, 11, 245, 14, 504, 18, 1026, 21, 2073, 22, 4168, 24, 8360, 25, 16745, 27, 33517, 28, 67062, 29, 134153, 30, 268336, 32, 536704, 33, 1073441, 35, 2146917, 37, 4293871, 39, 8587781, 40, 17175602, 41, 34351245, 45, 68702535, 47
Offset: 0

Views

Author

Reinhard Zumkeller, Sep 16 2014

Keywords

Comments

a(n) = A024431(n+1) - A024431(n) = A115409(n+1,n+1).

Links

Crossrefs

Cf. A024431, A115409.

Programs

  • Haskell
    a247414 n = a247414_list !! n
a247414_list = zipWith (-) (tail a024431_list) a024431_list

A115409 Inverse integer permutation of A115408.

Original entry on oeis.org

1, 5, 4, 7, 6, 2, 17, 16, 12, 10, 20, 19, 15, 13, 3, 43, 42, 38, 36, 26, 23, 51, 50, 46, 44, 34, 31, 8, 105, 104, 100, 98, 88, 85, 62, 54, 114, 113, 109, 107, 97, 94, 71, 63, 9
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 22 2006

Keywords

Comments

Seen as a triangle read by rows T(n,k) = a(n*(n-1)/2+k) = A024431(n)-A024431(k-1), 1<=k<=n.
T(n,1) = A024431(n)-1; T(n,n) = A247414(n-1). - Reinhard Zumkeller, Sep 16 2014

Examples

			Triangle begins:
1;
5, 4;
7, 6, 2;
17, 16, 12, 10;
20, 19, 15, 13, 3;
...

Links

Crossrefs

Cf. A024431, A115408, A247414.

Programs

  • Haskell
    import Data.List (inits)
a115409 n k = a115409_tabl !! (n-1) !! (k-1)
a115409_row n = a115409_tabl !! (n-1)
a115409_tabl = map f $ drop 2 $ inits a024431_list where
   f xs = reverse $ map (z -) zs where (z:zs) = reverse xs
a115409_list = concat a115409_tabl
-- Reinhard Zumkeller, Sep 16 2014
  • Mathematica
    nmax = 9;
differenceQ[seq_, x_] := Module[{r = False}, Do[If[x==seq[[k]] - seq[[j]], r = True; Break[]], {j, 1, Length[seq]}, {k, 1, Length[seq]}]; r];
seq[1] = {1, 2};
seq[i_] := seq[i] = Module[{j, k}, k = Max[seq[i-1]]; j = First[Select[ Range[k], !differenceQ[seq[i-1], #]&, 1]]; Union[seq[i-1], {2k+2, 2k+2+j}]];
A024431 = seq[nmax];
T[n_, k_] := A024431[[n+1]] -  A024431[[k]];
Table[T[n, k], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 20 2021 *)

A049399 A generalized difference set on the set of all integers (lambda = 2).

Original entry on oeis.org

1, 2, 6, 7, 16, 18, 38, 40, 82, 85, 172, 175, 352, 356, 714, 720, 1442, 1449, 2900, 2907, 5816, 5824, 11650, 11658, 23318, 23327, 46656, 46666, 93334, 93345, 186692, 186704, 373410, 373423, 746848, 746861, 1493724, 1493738, 2987478, 2987493, 5974988, 5975004
Offset: 0

Views

Author

Otokar Grosek (grosek(AT)elf.stuba.sk)

Keywords

Comments

In the set of all positive differences of the sequence each integer appears exactly twice, i.e., lambda = 2.
One could try to greedily build such a difference set as follows: b(1) = 1, b(n+1) = b(n)+j with j the smallest difference yet to appear twice. This would begin with {1, 2, 3, 5, 8, 12, 17, 23, 31, 39, 49} and fail; the smallest difference yet to appear twice is then 12 = 17-5, but 49+12 = 61 and 61-39 = 22 = 23-1 = 39-17. - Danny Rorabaugh, Sep 27 2015

Links

Crossrefs

Cf. A024431.

Formula

Let N_1={1, 2}. Given N_i, let N_{i+1} = N_i union {2k+2, 2k+2+j} where k = max element of N_i and j = smallest number of form x-y for at most one pair x, y in N_i, x>y. Union of all N_i gives sequence. - Danny Rorabaugh (mirroring formula in A024431), Sep 27 2015

Extensions

a(12)-a(15) corrected and more terms added by Danny Rorabaugh, Sep 27 2015
Showing 1-6 of 6 results.

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

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