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.

A218606 a(n) = A218608(n-1) + 1.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 10, 11, 13, 15, 16, 22, 24, 25, 39, 41, 42, 62, 63, 64, 65, 69, 71, 72, 92, 93, 94, 95, 105, 106, 107, 108, 114, 123, 125, 126, 146, 147, 148, 149, 159, 160, 161, 162, 168, 183, 184, 185, 186, 192, 203, 221, 223, 224, 244, 245, 246, 247, 257
Offset: 1

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Author

Antti Karttunen, Nov 03 2012

Keywords

Comments

These are the points i for which the predecessor node (i.e. the vertex that is one step towards the root) in the infinite trunk of beanstalk (A179016(i)) is at the greatest possible position of the allotted "window" which it at that point must pass through. (See comments at A218604.)

Links

Crossrefs

Cf. A218604, A218605, A218608.

Programs

Formula

a(n) = A218608(n-1) + 1.

Extensions

Definition changed because of the changed offset of A218604. - Antti Karttunen, Nov 10 2012

A173601 Greatest inverse of A071542, i.e., a(n) = maximal i such that A071542(i) = n.

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 11, 15, 17, 19, 23, 27, 31, 33, 35, 39, 43, 47, 51, 55, 59, 63, 65, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 125, 127, 129, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 189, 191, 195, 199, 203, 207
Offset: 0

Views

Author

Charles R Greathouse IV, Oct 30 2012

Keywords

Comments

What is s = lim sup a(n)/(n log_2(n))? A counting argument suggests s >= 1/2, and in any case s <= 1.
Essentially also the partial sums of A086876. - Antti Karttunen, Nov 10 2012 (per personal mail from Carl R. White, Nov 02 2012)

Links

Crossrefs

See A213708 for the least inverse. A086876 gives the first differences. Also, a(n)=A213708(n)+A086876(n)-1. Cf. A071542, A179016, A218604, A218608.

Programs

  • PARI
    v=vectorsmall(10^3);v[1]=1;for(n=2,#v,v[n]=v[n-hammingweight(n)]+1); u=vector(solve(x=1,#v,x*log(x)/log(2)-#v)\1);for(i=1,#v,if(v[i]<=#u,u[v[i]]=i)); u
  • Scheme
    ;; With Antti Karttunen's intseq-library:
(define A173601 (PARTIALSUMS 1 0 (compose-funs A086876 1+)))

Formula

a(n)/log_2(a(n)) < n < a(n) for n > 1.

Extensions

Changed the starting offset by prepending a(0)=0 (with the indexing of the rest of terms thus not changed) - Antti Karttunen, Nov 10 2012

A218604 a(n) = A173601(n) - A179016(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 2, 0, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 5, 0, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 5, 1, 2, 2, 3, 2, 2, 0, 0, 0, 0, 1, 3, 2, 0, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 5, 1, 2
Offset: 0

Views

Author

Antti Karttunen, Nov 03 2012

Keywords

Comments

For all n, the following holds: A213708(n) <= A179016(n) <= A173601(n). This sequence gives the distance of the node n in the infinite trunk of beanstalk (A179016(n)) from the greater edge of the A086876(n) wide window which it at that point must pass through.
The increasing steps seem to be quite constrained in their magnitude, compared to the decreasing steps. (This depends on how the "tendrils",i.e. the finite side-trees on the other side of the infinite trunk grow and reach their tops).

Links

Crossrefs

Positions of zeros: A218608, A218606.
Cf. A086876, A173601, A179016, A218603.

Programs

Formula

a(n) = A086876(n) - A218603(n) - 1.

Extensions

Offset changed because of the changed offset of A179016 - Antti Karttunen, Nov 10 2012

A218607 The positions of zeros in A218603, i.e., those integers i for which A179016(i) = A213708(i).

Original entry on oeis.org

0, 1, 3, 5, 8, 13, 22, 33, 35, 36, 37, 39, 50, 52, 53, 54, 55, 58, 69, 80, 82, 83, 84, 85, 88, 101, 118, 123, 134, 136, 137, 138, 139, 142, 155, 172, 179, 196, 207, 212, 221, 232, 234, 235, 236, 237, 240, 253, 270, 277, 294, 305, 310, 321, 338, 349, 354, 369, 374, 383, 400
Offset: 0

Views

Author

Antti Karttunen, Nov 10 2012

Keywords

Comments

These are the points i for which the corresponding node in the infinite trunk of beanstalk (A179016(i)) is at the least possible position of its allotted "window" which it at that point must pass through, i.e., there are no leaves or side-trees at its left (lesser) side at these points. (See comments at A218603.)

Links

Crossrefs

Apart from first two terms, a subset of A213732. Cf. A218608, A218605.
Showing 1-4 of 4 results.

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