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A373671 Length of the n-th maximal antirun of prime-powers.

%I A373671 #10 Jun 15 2024 16:34:39
%S A373671 1,1,1,2,1,4,7,26,27,1007,5558,5734,31209
%N A373671 Length of the n-th maximal antirun of prime-powers.
%C A373671 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 A373671 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%F A373671 Partial sums are A025528(A006549(n)).
%e A373671 The maximal antiruns of prime-powers begin:
%e A373671    2
%e A373671    3
%e A373671    4
%e A373671    5   7
%e A373671    8
%e A373671    9  11  13  16
%e A373671   17  19  23  25  27  29  31
%t A373671 Length/@Split[Select[Range[100],PrimePowerQ[#]&],#1+1!=#2&]//Most
%Y A373671 For prime antiruns we have A027833.
%Y A373671 For nonsquarefree runs we have A053797, firsts A373199.
%Y A373671 For non-prime-powers runs we have A110969, firsts A373669, sorted A373670.
%Y A373671 For squarefree runs we have A120992.
%Y A373671 For prime-power runs we have A174965.
%Y A373671 For prime runs we have A175632.
%Y A373671 For composite runs we have A176246, firsts A073051, sorted A373400.
%Y A373671 For squarefree antiruns we have A373127, firsts A373128.
%Y A373671 For composite antiruns we have A373403.
%Y A373671 For antiruns of prime-powers:
%Y A373671 - length A373671 (this sequence)
%Y A373671 - min A120430
%Y A373671 - max A006549
%Y A373671 For antiruns of non-prime-powers:
%Y A373671 - length A373672
%Y A373671 - min A373575
%Y A373671 - max A255346
%Y A373671 A000961 lists the powers of primes (including 1).
%Y A373671 A025528 counts prime-powers up to n.
%Y A373671 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373671 A361102 lists the non-prime-powers (not including 1 A024619).
%Y A373671 Cf. A000040, A001359, A008864, A014963, A038664, A054265, A067774, A251092, A373401.
%K A373671 nonn,more
%O A373671 1,4
%A A373671 _Gus Wiseman_, Jun 14 2024