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.

A357388 Numbers k such that A071626(k) < A071626(k+1).

Original entry on oeis.org

1, 3, 5, 9, 14, 21, 32, 43, 54, 65, 67, 84, 101, 115, 118, 135, 144, 152, 173, 202, 221, 231, 258, 260, 289, 295, 318, 332, 347, 369, 376, 405, 409, 423, 434, 450, 476, 491, 530, 532, 573, 589, 614, 648, 655, 696, 707, 736, 737, 766, 778, 803, 819, 825, 860, 870
Offset: 1

Views

Author

Amiram Eldar, Sep 26 2022

Keywords

Comments

Conjecture: This sequence has an asymptotic density 0.028..., which is the same as the asymptotic density of A357390 (see A357385).

Examples

			1 is a term since A071626(1) = 0 < A071626(2) = 1.

Links

Crossrefs

Cf. A071626, A342091, A357385, A357390.

Programs

  • Mathematica
    s[n_] := Length[Union[FactorInteger[n!][[;; , 2]]]]; s[1] = 0; Select[Range[1000], s[#] < s[# + 1] &]

A357390 Numbers k such that A071626(k) > A071626(k+1).

Original entry on oeis.org

64, 113, 132, 151, 216, 247, 278, 309, 340, 371, 402, 422, 433, 469, 515, 558, 601, 644, 687, 730, 731, 773, 792, 816, 853, 859, 914, 975, 1021, 1036, 1094, 1097, 1129, 1156, 1158, 1167, 1219, 1240, 1242, 1244, 1280, 1313, 1327, 1341, 1355, 1386, 1402, 1410, 1459
Offset: 1

Views

Author

Amiram Eldar, Sep 26 2022

Keywords

Comments

Conjecture: This sequence has an asymptotic density 0.028..., which is the same as the asymptotic density of A357388 (see A357385).

Examples

			64 is a term since A071626(64) = 9 > A071626(65) = 8.

Links

Crossrefs

Cf. A071626, A342091, A357385, A357388.

Programs

  • Mathematica
    s[n_] := Length[Union[FactorInteger[n!][[;; , 2]]]]; s[1]=0; Select[Range[1500], s[#] > s[# + 1] &]

A357389 a(n) is the start of the least run of exactly n consecutive positive integers with strictly increasing values of A071626, or -1 if no such run exists.

Original entry on oeis.org

7, 1, 736, 26048, 991434
Offset: 1

Views

Author

Amiram Eldar, Sep 26 2022

Keywords

Comments

a(n) is the least number k such that A071626(k) < A071626(k+1) < ... < A071626(k+n-1), but A071626(k-1) >= A071626(k) if k>1 and A071626(k+n-1) >= A071626(k+n).
a(6) > 10^7, if it exists.

Examples

			a(1) = 7 since 7 is the least positive integer that does not belong to a run of increasing values of A071626 with a length of at least 2.
a(3) = 736 since A071626(735) = A071626(736) = 26 < A071626(737) = 27 < A071626(738) = A071626(739) = 28, and 736 is the least number with this property.

Crossrefs

Cf. A071626, A342091, A357388, A357391.

A357391 a(n) is the start of the least run of exactly n consecutive positive integers with strictly decreasing values of A071626, or -1 if no such run exists.

Original entry on oeis.org

1, 64, 730, 8755, 12734, 8419585
Offset: 1

Views

Author

Amiram Eldar, Sep 26 2022

Keywords

Comments

a(n) is the least number k such that A071626(k) > A071626(k+1) > ... > A071626(k+n-1), but A071626(k-1) <= A071626(k) if k>1 and A071626(k+n-1) <= A071626(k+n).

Examples

			a(2) = 64 since A071626(64) = 9 > A071626(65) = 8, and A071626(63) = A071626(66) = 9, and 64 is the least number with this property.

Crossrefs

Cf. A071626, A342091, A357389, A357390.
Showing 1-4 of 4 results.

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

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