A373671 - OEIS

%I #10 Jun 15 2024 16:34:39

%S 1,1,1,2,1,4,7,26,27,1007,5558,5734,31209

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

%C An antirun of a sequence (in this case A000961 without 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 A025528(A006549(n)).

%e The maximal antiruns of prime-powers begin:

%e    2

%e    3

%e    4

%e    5   7

%e    8

%e    9  11  13  16

%e   17  19  23  25  27  29  31

%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 (this sequence)

%Y - min A120430

%Y - max A006549

%Y For antiruns of non-prime-powers:

%Y - length A373672

%Y - min A373575

%Y - max A255346

%Y A000961 lists the powers of primes (including 1).

%Y A025528 counts prime-powers up to n.

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

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

%Y Cf. A000040, A001359, A008864, A014963, A038664, A054265, A067774, A251092, A373401.

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Jun 14 2024