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.

A089118 Nonnegative numbers in (3*A005836 - 1) [A005836 are the numbers with base representation containing no 2].

Original entry on oeis.org

2, 8, 11, 26, 29, 35, 38, 80, 83, 89, 92, 107, 110, 116, 119, 242, 245, 251, 254, 269, 272, 278, 281, 323, 326, 332, 335, 350, 353, 359, 362, 728, 731, 737, 740, 755, 758, 764, 767, 809, 812, 818, 821, 836, 839, 845, 848, 971, 974, 980, 983, 998, 1001, 1007, 1010
Offset: 1

Views

Author

Emeric Deutsch and Bruce E. Sagan, Dec 05 2003

Keywords

Comments

Numbers k such that the Motzkin number A001006(k) == 2 (mod 3).

Links

Crossrefs

Cf. A005836, A001006, A082575, A089119.

Programs

  • Mathematica
    (* m = MotzkinNumber *) m[0] = 1; m[n_] := m[n] = m[n - 1] + Sum[ m[k]*m[n - 2 - k], {k, 0, n - 2}]; Select[ Range[1010], Mod[m[#], 3] == 2 &] (* Jean-François Alcover, Jul 10 2013 *)
Select[3*Range[350] - 1, DigitCount[# + 1, 3, 2] == 0 &] (* Amiram Eldar, Jun 04 2022 *)

Extensions

Offset corrected to 1 by Jean-François Alcover, Jun 23 2016

A082575 Nonnegative numbers in (3*A005836) union (3*A005836 - 2) [A005836 lists the numbers with base-3 representation containing no 2].

Original entry on oeis.org

0, 1, 3, 7, 9, 10, 12, 25, 27, 28, 30, 34, 36, 37, 39, 79, 81, 82, 84, 88, 90, 91, 93, 106, 108, 109, 111, 115, 117, 118, 120, 241, 243, 244, 246, 250, 252, 253, 255, 268, 270, 271, 273, 277, 279, 280, 282, 322, 324, 325, 327, 331, 333, 334, 336, 349, 351, 352
Offset: 1

Views

Author

Emeric Deutsch and Bruce E. Sagan, Dec 05 2003

Keywords

Comments

Numbers k such that the Motzkin number A001006(k) == 1 (mod 3).

Links

Crossrefs

Cf. A001006, A005836, A089118, A089119.

Programs

  • Mathematica
    (* m = MotzkinNumber *) m[0] = 1; m[n_] := m[n] = m[n - 1] + Sum[m[k]*m[n - 2 - k], {k, 0, n - 2}]; Select[Range[0, 400], Mod[m[#], 3] == 1 &] (* Jean-François Alcover, Jul 10 2013 *)
max = 150; Sort @ Join[Select[3*Range[0, max], DigitCount[#, 3, 2] == 0 &], Select[3*Range[max] - 2, DigitCount[# + 2, 3, 2] == 0 &]] (* Amiram Eldar, Jun 04 2022 *)

Extensions

Offset changed to 1 (sequence is a list) by L. Edson Jeffery, Nov 27 2015

A338220 Numbers k such that the Motzkin number A001006(k) is divisible by 5.

Original entry on oeis.org

9, 13, 23, 34, 38, 59, 63, 84, 88, 99, 109, 113, 134, 138, 148, 159, 163, 184, 188, 209, 213, 224, 234, 238, 249, 259, 263, 273, 284, 288, 309, 313, 334, 338, 349, 359, 363, 373, 384, 388, 398, 409, 413, 434, 438, 459, 463, 474, 484, 488, 509, 513, 523, 534, 538
Offset: 1

Views

Author

Amiram Eldar, Jan 30 2021

Keywords

Comments

The asymptotic density of this sequence is 1/10. It is a disjoint union of 4 sequences: numbers of the form (5*i + 1)*5^(2*j) - 2, (5*i + 2)*5^(2*j-1) - 1, (5*i + 3)*5^(2*j-1) - 2, and (5*i + 4)*5^(2*j) - 1, with i>=0 and j>=1, whose asymptotic densities are 1/120, 1/24, 1/24, and 1/120, respectively (Burns, 2016).

Examples

			9 is a term since A001006(9) = 835 = 5 * 167 is divisible by 5.

Links

Crossrefs

Cf. A001006.
Similar sequences, indices of Motzkin numbers divisible by m: A081706 (m = 2), A089119 (m = 3).

Programs

  • Mathematica
    motz[0] = motz[1] = 1; motz[n_] := motz[n] = ((2*n + 1)*motz[n - 1] + 3*(n - 1)*motz[n - 2])/(n + 2);  Select[Range[0, 500], Divisible[motz[#], 5] &]
Showing 1-3 of 3 results.

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

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