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 1-5 of 5 results.

A114890 First differences of A114889.

Original entry on oeis.org

2, 1, 3, 2, 1, 1, 1, 1, 6, 2, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 2, 1, 3, 2, 1, 1, 1, 1, 6, 2, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 42, 2, 1, 3, 2, 1, 1, 1, 1, 6, 2, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

John W. Layman, Jan 04 2006

Keywords

Crossrefs

Cf. A114889.

Formula

Conjecture. a(1)=2 and, for n>1, a(n)=1+3+9+...+3^(k-1) + 2, if n=3^k, a(n)=a(n-3^k), if 3^k < n < 2*3^k - 1, else a(n)=1. (This has been verified for n<=3000.)

A118374 Lexicographically earliest positive integer sequence no two terms of which sum to a term of {1,7,23,63,159,...} = {n*2^n-1}, n=1,2,3,... The first differences are given in A119350.

Original entry on oeis.org

1, 2, 3, 7, 8, 9, 10, 11, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 41, 42, 43, 47, 48, 49, 50, 51, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 97, 98, 99, 103, 104, 105, 106, 107, 113, 114, 115, 119, 120, 121, 122, 123, 124, 125
Offset: 1

Views

Author

John W. Layman, May 15 2006

Keywords

Comments

a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n)+a(i) is not of the form k*2^k-1 for i=1,..., n-1 and for any integer k>0.

Crossrefs

Cf. A114889, A119350.

Formula

It appears that a(n)=a(n-1)+A119350(n).

A119350 First differences of A118374.

Original entry on oeis.org

1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

John W. Layman, May 23 2006

Keywords

Crossrefs

Cf. A118374, A114889, A114890.

Formula

Conjecture. Define g(1)=1 and, for i>1, g(i)=2*g(i-1)+2^(i-2). Also define h(1)=1, h(2)=4 and, for i>2, h(i)=h(i-1)+2^(i-2). Then a(n)=h(i) if n=g(i), a(n)=1 if g(i)-2^(i-2)<=n

A138683 a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n) and a(k) do not sum to a term of A001333 (Numerators of continued fraction convergents to sqrt(2)).

Original entry on oeis.org

2, 3, 6, 7, 8, 12, 13, 16, 17, 18, 19, 20, 26, 27, 30, 31, 32, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 64, 65, 66, 70, 71, 74, 75, 76, 77, 78, 84, 85, 88, 89, 90, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115
Offset: 1

Views

Author

John W. Layman, Mar 26 2008

Keywords

Comments

The graph of the first differences (A138684) of this sequence is fractal-like.

Crossrefs

Cf. A001333, A005652, A114889, A138684.

A138684 First differences of A138683.

Original entry on oeis.org

1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 3, 1, 1, 4, 1
Offset: 1

Views

Author

John W. Layman, Mar 26 2008

Keywords

Comments

The graph of this sequence is fractal-like.
Conjecture. Let x(1)=1, x(2)=2, x(n) = 2*x(n-1) + x(n-2), and let y(1)=1, y(2)=3, y(n) = y(n-1) + y(n-2). Then if n=x(k), a(n)=y(k); if x(k) < n < 2*x(k), a(n) = a(n-x(k)); and if 2*x(k) <= n < x(k+1), a(n)=1. (This has been confirmed for n < 500.) - John W. Layman, Nov 26 2011

Crossrefs

Cf. A114889, A114890, A138683.
Showing 1-5 of 5 results.

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