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 1-3 of 3 results.

A268678 Distinct values in A268395; partial sums of A268679.

Original entry on oeis.org

0, 1, 3, 4, 5, 7, 8, 11, 15, 16, 18, 19, 20, 22, 23, 26, 27, 31, 32, 34, 36, 37, 40, 41, 42, 47, 48, 50, 52, 53, 56, 57, 59, 60, 64, 65, 66, 69, 70, 72, 74, 75, 81, 82, 83, 86, 87, 89, 90, 92, 93, 98, 101, 102, 104, 105, 106, 108, 109, 113, 116, 117, 119, 120, 121, 123, 124, 127, 131, 132, 134, 135, 136, 138, 139, 142
Offset: 0

Views

Author

Antti Karttunen, Feb 10 2016

Keywords

Links

Crossrefs

Cf. A001969, A268395, A268679.
Cf. A268677 (complement).
Cf. A268680 (least monotonic left inverse).
Cf. A268712.
Cf. also A004128.

Programs

  • Mathematica
    f[n_] := Which[n == 1, 0, OddQ@ #, 0, EvenQ@ #, 1 + f[#/2]] &@ Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; Union@ Accumulate@ Array[f, {150}] (* Michael De Vlieger, Feb 12 2016, after Jan Mangaldan at A006068 *)

Formula

a(0) = 0, for n >= 1, a(n) = A268679(n) + a(n-1).
a(n) = A268395(A001969(1+n)).
Other identities. For all n >= 0:
A268680(a(n)) = n.

A268677 Complement of A268678; numbers that do not occur in A268395.

Original entry on oeis.org

2, 6, 9, 10, 12, 13, 14, 17, 21, 24, 25, 28, 29, 30, 33, 35, 38, 39, 43, 44, 45, 46, 49, 51, 54, 55, 58, 61, 62, 63, 67, 68, 71, 73, 76, 77, 78, 79, 80, 84, 85, 88, 91, 94, 95, 96, 97, 99, 100, 103, 107, 110, 111, 112, 114, 115, 118, 122, 125, 126, 128, 129, 130, 133, 137, 140, 141, 143, 144, 145, 146, 149, 152
Offset: 1

Views

Author

Antti Karttunen, Feb 10 2016

Keywords

Links

Crossrefs

Cf. A268395, A268678.
Cf. A268712.
Cf. also A096346.

Programs

  • Mathematica
    f[n_] := Which[n == 1, 0, OddQ@ #, 0, EvenQ@ #, 1 + f[#/2]] &@ Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; Complement[Range@ #, Union@ Accumulate@ Array[f, {#}]] &@ 152 (* Michael De Vlieger, Feb 12 2016, after Jan Mangaldan at A006068 *)

A268711 Permutation of natural numbers: a(1) = 1, a(A268677(n)) = 2*a(n), a(A268678(n+1)) = 1+(2*a(n)).

Original entry on oeis.org

1, 2, 3, 5, 7, 4, 11, 15, 6, 10, 9, 14, 8, 22, 23, 31, 30, 13, 21, 19, 12, 29, 17, 20, 18, 45, 47, 28, 16, 44, 63, 61, 46, 27, 62, 43, 39, 60, 26, 25, 59, 35, 42, 38, 24, 58, 41, 37, 34, 91, 40, 95, 57, 36, 90, 33, 89, 94, 127, 123, 56, 32, 88, 93, 55, 125, 126, 122, 87, 79, 92, 121, 54, 53, 51, 124, 86, 78, 120
Offset: 1

Views

Author

Antti Karttunen, Feb 11 2016

Keywords

Links

Crossrefs

Inverse: A268712.
Cf. A268677, A268678, A268680.

Formula

a(1) = 1, for n > 1: if A268680(n) = A268680(n-1) [when n is in A268677] a(n) = 2*a(n-A268680(n)), otherwise [when n is in A268678] a(n) = 1 + 2*a(A268680(n)-1).
Showing 1-3 of 3 results.

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

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