A373410 Minimum of the n-th maximal 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

Offset: 1

Author

Gus Wiseman, Jun 06 2024

Keywords

• nonn

Comments

The maximum is given by A068781.

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.

Examples

			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
		

Links

• Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers

Crossrefs

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. A049094, A061399, A077641, A077643, A112926, A143658, A294242, A350842, A372683, A372684, A373125.

Programs

Mathematica

First/@Split[Select[Range[100],!SquareFreeQ[#]&],#1+1!=#2&]

Formula

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