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.

A268713 Positions of records in A268672.

Original entry on oeis.org

0, 1, 2, 4, 8, 13, 14, 44, 50, 84, 134, 220, 234, 253, 254, 764, 1274, 2294, 3822, 8414, 13106, 21742, 30581, 30582, 34678, 56796, 60094, 65020, 65262, 65533, 65534, 196604, 327674, 589814, 983022
Offset: 0

Views

Author

Antti Karttunen, Feb 12 2016

Keywords

Comments

a(n) seems also to be the first position k in A268672 where A268672(k) = n (when a(0) = 0, which is the reason the starting offset is 0 instead of 1).

Crossrefs

Cf. A001317, A268672.

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).

A268708 Number of iterations of A268395 needed to reach zero: a(0) = 0, for n >= 1, a(n) = 1 + a(A268395(n)).

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18
Offset: 0

Views

Author

Antti Karttunen, Feb 11 2016

Keywords

Comments

Set k = n, take the k-th Xfactorial A048631(k) and find what is the maximum exponent h so that polynomial (X+1)^h still divides it (over GF(2), this can be computed with A268389, maybe also more directly). Set this h as a new value of k, and repeat. a(n) tells how many steps are needed before zero is reached.
Note that so far it is just an empirical observation that A268672(n) > 0 for all n > 0.

Links

Crossrefs

Cf. A048631, A268389, A268395, A268672.
Cf. also A268709, A268710.

Formula

a(0) = 0, for n >= 1, a(n) = 1 + a(A268395(n)).
Showing 1-3 of 3 results.

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

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