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A373675 Sums of maximal runs of powers of primes A000961.

%I A373675 #7 Jun 16 2024 15:23:10
%S A373675 15,24,11,13,33,19,23,25,27,29,63,37,41,43,47,49,53,59,61,64,67,71,73,
%T A373675 79,81,83,89,97,101,103,107,109,113,121,125,255,131,137,139,149,151,
%U A373675 157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239
%N A373675 Sums of maximal runs of powers of primes A000961.
%C A373675 A run of a sequence (in this case A000961) is an interval of positions at which consecutive terms differ by one.
%H A373675 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373675 The maximal runs of powers of primes begin:
%e A373675    1   2   3   4   5
%e A373675    7   8   9
%e A373675   11
%e A373675   13
%e A373675   16  17
%e A373675   19
%e A373675   23
%e A373675   25
%e A373675   27
%e A373675   29
%e A373675   31  32
%e A373675   37
%e A373675   41
%e A373675   43
%e A373675   47
%e A373675   49
%t A373675 pripow[n_]:=n==1||PrimePowerQ[n];
%t A373675 Total/@Split[Select[Range[nn],pripow],#1+1==#2&]//Most
%Y A373675 A000040 lists the primes, differences A001223.
%Y A373675 A000961 lists all powers of primes (A246655 if not including 1).
%Y A373675 A025528 counts prime-powers up to n.
%Y A373675 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373675 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A373675 See link for composite, prime, nonsquarefree, and squarefree runs.
%Y A373675 Prime-power runs: A373675, min A373673, max A373674, length A174965.
%Y A373675 Non-prime-power runs: A373678, min A373676, max A373677, length A110969.
%Y A373675 Prime-power antiruns: A373576, min A120430, max A006549, length A373671.
%Y A373675 Non-prime-power antiruns: A373679, min A373575, max A255346, length A373672.
%Y A373675 Cf. A005117, A014963, A029707, A038664, A046933, A054265, A065855, A071148, A293697, A371201.
%K A373675 nonn
%O A373675 1,1
%A A373675 _Gus Wiseman_, Jun 16 2024