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.

A268709 Number of iterations of A268395 needed to reach zero from 2^n: a(n) = A268708(2^n).

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 25, 40, 75, 134, 246, 428, 802, 1453, 2643, 4587, 8851, 16849, 32368, 60503, 117343
Offset: 0

Views

Author

Antti Karttunen, Feb 11 2016

Keywords

Crossrefs

Cf. A000079, A268395, A268708, A268710.

Programs

Formula

a(n) = A268708(2^n).

A268710 Number of iterations of A268395 needed to reach zero from 2^n + 1: a(n) = A268708(2^n + 1).

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 15, 25, 41, 75, 134, 246, 428, 802, 1454, 2643, 4588, 8851, 16849, 32368, 60504, 117343
Offset: 0

Views

Author

Antti Karttunen, Feb 11 2016

Keywords

Crossrefs

Cf. A000051, A268395, A268708, A268709.

Programs

Formula

a(n) = A268708((2^n)+1).

A268395 Partial sums of A268389.

Original entry on oeis.org

0, 0, 0, 1, 1, 3, 4, 4, 4, 5, 7, 7, 8, 8, 8, 11, 11, 15, 16, 16, 18, 18, 18, 19, 20, 20, 20, 22, 22, 23, 26, 26, 26, 27, 31, 31, 32, 32, 32, 34, 36, 36, 36, 37, 37, 40, 41, 41, 42, 42, 42, 47, 47, 48, 50, 50, 50, 52, 53, 53, 56, 56, 56, 57, 57, 59, 60, 60, 64, 64, 64, 65, 66, 66, 66, 69, 69, 70, 72, 72, 74, 74, 74, 75, 75, 81
Offset: 0

Views

Author

Antti Karttunen, Feb 10 2016

Keywords

Links

Crossrefs

Cf. A048631, A268389, A268672.
Cf. A268678 (with duplicates removed), A268677 (numbers that do not occur here).
Cf. A268708, A268709, A268710.
Cf. also A054861.

Programs

  • Mathematica
    f[n_] := Which[n == 1, 0, OddQ@ #, 0, EvenQ@ #, 1 + f[#/2]] &@ Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; Accumulate@ Array[f, {85}] (* Michael De Vlieger, Feb 12 2016, after Jan Mangaldan at A006068 *)

Formula

a(0) = 0, for n >= 1, a(n) = A268389(n) + a(n-1).
Other identities. For all n >= 0:
a(n) = A268389(A048631(n)).
a(n) = n - A268672(n).

A268672 a(n) = n - A268395(n).

Original entry on oeis.org

0, 1, 2, 2, 3, 2, 2, 3, 4, 4, 3, 4, 4, 5, 6, 4, 5, 2, 2, 3, 2, 3, 4, 4, 4, 5, 6, 5, 6, 6, 4, 5, 6, 6, 3, 4, 4, 5, 6, 5, 4, 5, 6, 6, 7, 5, 5, 6, 6, 7, 8, 4, 5, 5, 4, 5, 6, 5, 5, 6, 4, 5, 6, 6, 7, 6, 6, 7, 4, 5, 6, 6, 6, 7, 8, 6, 7, 7, 6, 7, 6, 7, 8, 8, 9, 4, 4, 5, 6, 6, 4, 5, 5, 6, 7, 6, 6, 7, 8, 7, 8, 8, 4, 5, 6, 4, 4, 5, 4, 5, 6, 6, 7, 7, 6, 7, 7, 8, 9, 6, 4
Offset: 0

Views

Author

Antti Karttunen, Feb 10 2016

Keywords

Comments

It seems that the sequence stays strictly positive after a(0).
Only 1 seems to be at a(1).
2's occur in this sequence at least in the following positions: 2, 3, 5, 6, 17, 18, 20, 257, 258, 260, 272, 65537, 65538, 65540, 65552, 65792, and in no other location up to 2^21.
See also comments in A268708.

Links

Crossrefs

Cf. A001317, A268395, A268708.
Cf. A268713 (record positions).

Programs

Formula

a(n) = n - A268395(n).
Showing 1-4 of 4 results.

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

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