proposed

approved

editing

proposed

Minimum of the n-th maximal antirun of nonsquarefree numbers differing by more than one.

The maximum is A068781. The length of this run is given by A373409A068781.

An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.

Consists of 4 and all nonsquarefree numbers n such that n - 1 is also nonsquarefree.

a(1) = 4; a(n>1) = A068781(n-1) + 1.

First/@Split[Select[Range[1000100], !SquareFreeQ[#]&], #1+1!=#2&]

Cf. A008864, `A025157, A049093, A049094, `A049095, `A061398, A061399, A077641, A077643, A101836, `A112925, A112926, A143658, A294242, A350842, A372683, A372684, A373125.

Cf. A372683, A372684, `A373123, A373125, `A373126, `A373197, `A373198.

Cf. A008864, `A025157, A049093, A049094, `A049095, `A061398, A061399, A077641, A077643, A101836, `A112925, A112926, A143658, A294242, A350842.

allocated for Gus WisemanMinimum of the n-th antirun of nonsquarefree numbers differing by more than one.

4, 9, 25, 28, 45, 49, 50, 64, 76, 81, 99, 100, 117, 121, 125, 126, 136, 148, 153, 169, 172, 176, 189, 208, 225, 243, 244, 245, 261, 276, 280, 289, 297, 316, 325, 333, 343, 344, 351, 352, 361, 364, 369, 376, 388, 405, 424, 425, 441, 460, 476, 477, 496, 508, 513

1,1

The maximum is A068781. The length of this run is given by A373409.

Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>

Row-minima of:

4 8

9 12 16 18 20 24

25 27

28 32 36 40 44

45 48

49

50 52 54 56 60 63

64 68 72 75

76 80

81 84 88 90 92 96 98

99

First/@Split[Select[Range[1000], !SquareFreeQ[#]&], #1+1!=#2&]

Functional neighbors: A005381, A006512, A053806, A068781, A373408, A373409, A373412.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A008864, `A025157, A049093, A049094, `A049095, `A061398, A077641, A077643, A101836, `A112925, A112926, A143658, A350842.

Cf. A372683, A372684, `A373123, A373125, `A373126, `A373197, `A373198.

allocated

nonn

Gus Wiseman, Jun 06 2024

approved

editing

allocated for Gus Wiseman

allocated

approved