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A373674 Last element of each maximal run of powers of primes (including 1).

%I A373674 #8 Aug 02 2024 05:21:35
%S A373674 5,9,11,13,17,19,23,25,27,29,32,37,41,43,47,49,53,59,61,64,67,71,73,
%T A373674 79,81,83,89,97,101,103,107,109,113,121,125,128,131,137,139,149,151,
%U A373674 157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239
%N A373674 Last element of each maximal run of powers of primes (including 1).
%C A373674 A run of a sequence (in this case A000961) is an interval of positions at which consecutive terms differ by one.
%C A373674 The first element of the same run is A373673.
%C A373674 Consists of all powers of primes k such that k+1 is not a power of primes.
%H A373674 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373674 The maximal runs of powers of primes begin:
%e A373674    1   2   3   4   5
%e A373674    7   8   9
%e A373674   11
%e A373674   13
%e A373674   16  17
%e A373674   19
%e A373674   23
%e A373674   25
%e A373674   27
%e A373674   29
%e A373674   31  32
%e A373674   37
%e A373674   41
%e A373674   43
%e A373674   47
%e A373674   49
%t A373674 pripow[n_]:=n==1||PrimePowerQ[n];
%t A373674 Max/@Split[Select[Range[nn],pripow],#1+1==#2&]//Most
%Y A373674 For prime antiruns we have A001359, min A006512, length A027833.
%Y A373674 For composite runs we have A006093, min A008864, length A176246.
%Y A373674 For prime runs we have A067774, min A025584, length A251092 or A175632.
%Y A373674 For squarefree runs we have A373415, min A072284, length A120992.
%Y A373674 For nonsquarefree runs we have min A053806, length A053797.
%Y A373674 For runs of prime-powers:
%Y A373674 - length A174965
%Y A373674 - min A373673
%Y A373674 - max A373674 (this sequence)
%Y A373674 - sum A373675
%Y A373674 For runs of non-prime-powers:
%Y A373674 - length A110969 (firsts A373669, sorted A373670)
%Y A373674 - min A373676
%Y A373674 - max A373677
%Y A373674 - sum A373678
%Y A373674 For antiruns of prime-powers:
%Y A373674 - length A373671
%Y A373674 - min A120430
%Y A373674 - max A006549
%Y A373674 - sum A373576
%Y A373674 For antiruns of non-prime-powers:
%Y A373674 - length A373672
%Y A373674 - min A373575
%Y A373674 - max A255346
%Y A373674 - sum A373679
%Y A373674 A000961 lists all powers of primes (A246655 if not including 1).
%Y A373674 A025528 counts prime-powers up to n.
%Y A373674 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373674 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A373674 Cf. A000040, A005381, A007674, A014963, A068780, A068781, A073051, A373400.
%K A373674 nonn
%O A373674 1,1
%A A373674 _Gus Wiseman_, Jun 16 2024