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.

A266510 Partial sums of A266509.

Original entry on oeis.org

0, 0, 1, 2, 3, 4, 7, 10, 11, 12, 15, 18, 23, 28, 35, 42, 43, 44, 47, 50, 55, 60, 67, 74, 79, 84, 95, 106, 123, 140, 155, 170, 171, 172, 175, 178, 183, 188, 195, 202, 207, 212, 223, 234, 251, 268, 283, 298, 303, 308, 319, 330, 347, 364, 387, 410, 439, 468, 503, 538, 579, 620, 651, 682, 683, 684, 687, 690, 695, 700
Offset: 1

Views

Author

Omar E. Pol, Dec 30 2015

Keywords

Comments

Also A256265 and twice the terms of A256264 interleaved, with a(1) = 0.
It appears that this sequence has a fractal (or fractal-like) behavior.
First differs from A266530 at a(55), with which it shares infinitely many terms.
First differs from A266540 at a(25), with which it shares infinitely many terms.
For an illustration of initial terms consider the diagram of A256264 in the fourth quadrant of the square grid together with a reflected copy in the second quadrant.

Links

Crossrefs

Cf. A256263, A256264, A256265, A266509, A266530, A266540.

Programs

  • Mathematica
    Accumulate@Riffle[#, #] &@ Flatten@Join[{0}, NestList[Join[#, Range[ Length[ #] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 5]] (* Ivan Neretin, Feb 14 2017 *)

Formula

a(2n-1) = A256265(n).
a(2n) = 2 * A256264(n-1).
a(n) = (a(n-1) + a(n+1))/2, if n is an odd number greater than 1.

A266539 Terms of A006257 (Josephus problem) repeated.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 5, 5, 7, 7, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25
Offset: 1

Views

Author

Omar E. Pol, Jan 02 2016

Keywords

Comments

First differs from both A266509 and A266529 at a(25), and shares with them infinitely many terms.

Examples

			Written as an irregular triangle in which the row lengths are twice the terms of A011782 the sequence begins:
   0, 0;
   1, 1;
   1, 1, 3, 3;
   1, 1, 3, 3, 5, 5, 7, 7;
   1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15;
   ...
Row sums give 0 together with A004171.

Links

Crossrefs

Partial sums give A266540.
Cf. A004171, A006257, A011782, A256249, A266509, A266529, A266535.

Programs

  • Maple
    A006257[0]:=0: for n from 1 to 100 do A006257[n]:=(A006257[n-1]+1) mod n +1: end do:
seq(A006257[i]$2,i=0..100); # Robert Israel, Jan 13 2016
  • Mathematica
    Join[{0, 0}, Table[SeriesCoefficient[(1 + x^2)/((-1 + x)^2 (1 + x)), {x, 0, m}], {n, 6}, {m, 0, 2^n - 1}]] // Flatten (* Michael De Vlieger, Jan 05 2016 *)

Formula

G.f.: (x^2 + x^4)/(1 - x - x^2 + x^3) - (1 - x)^(-1)*Sum_{k>=1} 2^k*x^(2^(k+1)). - Robert Israel, Jan 13 2016

Extensions

Offset changed to 1 by Ivan Neretin, Feb 09 2017

A266529 Terms of A160552 repeated.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 5, 5, 7, 7, 1, 1, 3, 3, 5, 5, 7, 7, 5, 5, 11, 11, 17, 17, 15, 15, 1, 1, 3, 3, 5, 5, 7, 7, 5, 5, 11, 11, 17, 17, 15, 15, 5, 5, 11, 11, 17, 17, 19, 19, 21, 21, 39, 39, 49, 49, 31, 31, 1, 1, 3, 3, 5, 5, 7, 7, 5, 5, 11, 11, 17, 17, 15, 15, 5, 5, 11, 11, 17, 17, 19, 19, 21, 21
Offset: 1

Views

Author

Omar E. Pol, Jan 02 2016

Keywords

Comments

First differs from A266509 at a(55), with which it shares infinitely many terms.
First differs from A266539 at a(25), with which it shares infinitely many terms.

Examples

			Written as an irregular triangle in which the row lengths are twice the terms of A011782 the sequence begins:
0,0;
1,1;
1,1,3,3;
1,1,3,3,5,5,7,7;
1,1,3,3,5,5,7,7,5,5,11,11,17,17,15,15;
1,1,3,3,5,5,7,7,5,5,11,11,17,17,15,15,5,5,11,11,17,17,19,19,21,21,39,39,49,49,31,31;
...
Row sums give 0 together with A004171.

Links

Crossrefs

Partial sums give A266530.
Cf. A004171, A011782, A139250, A160552, A255747, A266509, A266539.

Programs

  • Mathematica
    Riffle[#, #] &@ Table[SeriesCoefficient[x (1 + 2 x)/(1 + x) + (4 x^2/(1 + 2 x)) (Product[1 + x^(2^k - 1) + 2 x^(2^k), {k, 20}] - 1), {x, 0, n}], {n, 0, 44}] (* Michael De Vlieger, Jan 05 2016, based on Maple by N. J. A. Sloane at A160552 *)
Showing 1-3 of 3 results.

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

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