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.

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A276343 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A005187(1+a(n)), a(A088359(n)) = A055938(a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 9, 10, 8, 31, 30, 29, 28, 27, 26, 24, 20, 25, 21, 23, 22, 17, 18, 19, 16, 63, 62, 61, 60, 59, 58, 57, 55, 51, 43, 56, 52, 44, 54, 48, 53, 50, 45, 36, 47, 37, 39, 49, 40, 41, 46, 42, 33, 34, 35, 38, 32, 127, 126, 125, 124, 123, 122, 121, 120, 118, 114, 106, 90, 119, 115, 107, 91, 117, 111, 99
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276344.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276345, A276441.
Compare also to the scatter-plots of A276443 and A276445.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A005187(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A055938(a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A267111(n)).
a(n) = A233278(A276441(n)).

A276345 Permutation of natural numbers: a(1) = 1, a(A087686(1+n)) = A055938(a(n)), a(A088359(n)) = A005187(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001.

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 6, 12, 10, 8, 15, 9, 11, 14, 13, 27, 23, 19, 16, 31, 21, 18, 22, 17, 26, 30, 20, 25, 24, 29, 28, 58, 53, 46, 38, 32, 63, 48, 41, 35, 42, 40, 34, 50, 33, 57, 62, 44, 39, 49, 37, 47, 45, 36, 56, 55, 61, 43, 54, 52, 51, 60, 59, 121, 113, 104, 89, 74, 64, 127, 108, 95, 81, 70, 82, 93, 79, 67, 98, 77, 66, 112, 65, 120
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276346.
Cf. A004001, A005187, A055938, A080677, A087686, A088359, A093879.
Similar or related permutations: A233276, A233278, A267111, A276343, A276441.

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A055938(a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A005187(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A233276(A276441(n)).
a(n) = A233278(A267111(n)).

A276443 Permutation of natural numbers: a(1) = 1, a(A087686(n)) = A000069(1+a(n-1)), a(A088359(n)) = A001969(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001, and A000069 & A001969 are odious & evil numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 15, 13, 14, 16, 17, 18, 20, 24, 19, 23, 30, 21, 27, 25, 22, 29, 31, 26, 28, 32, 33, 34, 36, 40, 48, 35, 39, 46, 60, 37, 43, 54, 41, 51, 49, 38, 45, 58, 47, 63, 61, 42, 53, 55, 50, 44, 57, 59, 62, 52, 56, 64, 65, 66, 68, 72, 80, 96, 67, 71, 78, 92, 120, 69, 75, 86, 108, 73, 83, 102, 81
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2016

Keywords

Links

Crossrefs

Inverse: A276444.
Cf. A000069, A001969, A004001, A080677, A087686, A088359, A093879.
Similar or related permutations: A003188, A276441, A276445 (compare the scatter plots).

Programs

Formula

a(1) = 1; for n > 1, if A093879(n-1) = 0 [when n is in A087686], a(n) = A000069(1+a(A080677(n)-1)), otherwise [when n is in A088359], a(n) = A001969(1+a(A004001(n)-1)).
As a composition of other permutations:
a(n) = A003188(A276441(n)).

A266188 a(n) = A004001(A087686(n)).

Original entry on oeis.org

1, 1, 2, 4, 4, 7, 8, 8, 8, 12, 14, 15, 15, 16, 16, 16, 16, 21, 24, 26, 27, 27, 29, 30, 30, 31, 31, 31, 32, 32, 32, 32, 32, 38, 42, 45, 47, 48, 48, 51, 53, 54, 54, 56, 57, 57, 58, 58, 58, 60, 61, 61, 62, 62, 62, 63, 63, 63, 63, 64, 64, 64, 64, 64, 64, 71, 76, 80, 83, 85, 86, 86, 90, 93, 95, 96, 96, 99, 101, 102, 102, 104
Offset: 1

Views

Author

Antti Karttunen, Jan 10 2016

Keywords

Comments

Discarding duplicates gives A087686 back, i.e., this set of numbers is closed with respect to A004001.

Links

Crossrefs

Cf. A004001, A080677, A087686.

Programs

Formula

a(n) = A004001(A087686(n)).

A283468 a(n) = A004001(A004001(n-1)) - A004001(n-A004001(n-1)), a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, -1, 0, 1, 2, 2, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 2, 3, 3, 2, 3, 4, 4, 3, 4, 4, 3, 3, 3, 2, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 3, 4, 4, 3, 4, 5, 6, 6, 5, 6, 7, 7, 6, 7, 7, 6, 6, 6, 5, 6, 7, 7, 6, 7, 7, 6, 6, 6, 5, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1
Offset: 1

Views

Author

Antti Karttunen, Mar 18 2017

Keywords

Comments

The only negative terms seem to be -1's, occurring as a(1+(2^n)), for n >= 2.

Links

Crossrefs

Cf. A004001, A080677, A283471 (positions of zeros), A283469, A283470, A283472.
Cf. also A283655.

Programs

Formula

a(1) = a(2) = 1; for n > 2, a(n) = A004001(A004001(n-1)) - A004001(A080677(n-1)).

A283677 a(n) = lcm(b(b(n)), b(n-b(n)+1)) where b(n) = A004001(n).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 6, 3, 12, 12, 4, 4, 4, 4, 20, 5, 30, 35, 35, 42, 24, 24, 56, 56, 56, 8, 8, 8, 8, 8, 72, 9, 90, 99, 36, 36, 60, 130, 70, 70, 154, 165, 165, 60, 60, 60, 195, 208, 208, 112, 112, 112, 240, 240, 240, 240, 16, 16, 16, 16, 16, 16, 272, 17, 306, 323, 340, 357, 357, 126, 198, 414, 72, 72, 456, 475, 494
Offset: 1

Views

Author

Altug Alkan, Mar 14 2017

Keywords

Comments

See the order of certain subsequences in scatterplot link.

Examples

			a(4) = lcm(A004001(A004001(4)), A004001(4-A004001(4)+1)) = lcm(1, 2) = 2.

Links

Crossrefs

Cf. A004001, A080677.
Cf. also A283470, A283673.

Programs

  • Mathematica
    b[1] = b[2] = 1; b[n_] := b[n] = b[b[n - 1]] + b[n - b[n - 1]]; Table[LCM[b[b[n]], b[n + 1 - b[n]]], {n, 1, 78}] (* Indranil Ghosh, Mar 14 2017 *)
  • PARI
    a=vector(1000); a[1]=a[2]=1; for(n=3, #a, a[n]=a[a[n-1]]+a[n-a[n-1]]); va = vector(1000, n, lcm(a[a[n]], a[n+1-a[n]]))
  • Scheme
    (define (A283677 n) (lcm (A004001 (A004001 n)) (A004001 (+ 1 (- n (A004001 n)))))) ;; (Code for A004001 given under that entry). - Antti Karttunen, Mar 18 2017

Formula

a(n) = lcm(A004001(A004001(n)), A004001(A080677(n))). - Antti Karttunen, Mar 18 2017

A087816 a(n) = a(a(n-1)) + a(n - 1 - a(n-1)) with a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 34
Offset: 1

Views

Author

Roger L. Bagula, Oct 05 2003

Keywords

Crossrefs

Cf. A004001, A055748, A080677, A087815.

Programs

  • Maple
    A087816 := proc(n) option remember; if n <= 2 then 1 else procname(procname(n-1)) + procname(n - 1 - procname(n-1)); fi; end;
seq(A087816(n), n = 1..100); # Peter Bala, Sep 11 2022
  • Mathematica
    hg[n_Integer?Positive] := hg[n] =hg[hg[n-1]] + hg[n -1- hg[n-1]] hg[1] = hg[2] = 1 digits=2^8 a=Table[hg[n], {n, 1, digits}]

Formula

From Peter Bala, Sep 11 2022: (Start)
a(n) = n + 1 - A004001(n+1).
a(n) = A080677(n+1) - 1.
a(n+1) - a(n) = 0 or 1. (End)
Previous Showing 11-17 of 17 results.

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