A357390 -id:A357390 - cp's OEIS frontend

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

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

Amiram Eldar, Sep 26 2022

nonn

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A071626, A342091, A357385, A357390.

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

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

Amiram Eldar, Sep 26 2022

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

Cf. A071626, A342091, A357389, A357390.

cp's OEIS Frontend

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

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