%I #12 Jun 20 2024 16:58:22

%S 5,3,1,6,1,1,2,1,3,1,3,1,2,1,1,1,3,2,2,1,3,1,1,1,4,1,1,1,2,1,1,1,1,1,

%T 2,1,3,1,3,1,2,1,1,1,1,1,2,1,3,2,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,2,1,1,

%U 1,2,1,3,1,2,1,1,1,3,1,1,1,1,1,1,1,3,1

%N Length of the n-th maximal antirun of non-prime-powers.

%C An antirun of a sequence (in this case A361102 or A024619 with 1) is an interval of positions at which consecutive terms differ by more than one.

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

%F Partial sums are A356068(A255346(n)).

%e The maximal antiruns of non-prime-powers begin:

%e 1 6 10 12 14

%e 15 18 20

%e 21

%e 22 24 26 28 30 33

%e 34

%e 35

%e 36 38

%e 39

%e 40 42 44

%e 45

%e 46 48 50

%t Length/@Split[Select[Range[100],!PrimePowerQ[#]&],#1+1!=#2&]//Most

%Y For prime antiruns we have A027833.

%Y For nonsquarefree runs we have A053797, firsts A373199.

%Y For non-prime-powers runs we have A110969, firsts A373669, sorted A373670.

%Y For squarefree runs we have A120992.

%Y For prime-power runs we have A174965.

%Y For prime runs we have A175632.

%Y For composite runs we have A176246, firsts A073051, sorted A373400.

%Y For squarefree antiruns we have A373127, firsts A373128.

%Y For composite antiruns we have A373403.

%Y For antiruns of prime-powers:

%Y - length A373671

%Y - min A120430

%Y - max A006549

%Y For antiruns of non-prime-powers:

%Y - length A373672 (this sequence), firsts (3,7,2,25,1,4)

%Y - min A373575

%Y - max A255346

%Y A000961 lists all powers of primes. A246655 lists just prime-powers.

%Y A057820 gives first differences of consecutive prime-powers, gaps A093555.

%Y A356068 counts non-prime-powers up to n.

%Y A361102 lists all non-prime-powers (A024619 if not including 1).

%Y Cf. A001359, A008864, A014963, A038664, A054265, A067774, A251092, A373401.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 14 2024