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

1,1

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.

Links

Table of n, a(n) for n=1..55.

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

Formula

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

Example

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

Mathematica

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

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.

Sequence in context: A340640 A073045 A045967 * A336445 A232241 A163836

Adjacent sequences: A373407 A373408 A373409 * A373411 A373412 A373413

Keyword

nonn

Author

Gus Wiseman, Jun 06 2024

Status

approved