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A373676 First element of each maximal run of non-prime-powers.

%I A373676 #9 Jun 17 2024 14:48:43
%S A373676 1,6,10,12,14,18,20,24,26,28,30,33,38,42,44,48,50,54,60,62,65,68,72,
%T A373676 74,80,82,84,90,98,102,104,108,110,114,122,126,129,132,138,140,150,
%U A373676 152,158,164,168,170,174,180,182,192,194,198,200,212,224,228,230,234
%N A373676 First element of each maximal run of non-prime-powers.
%C A373676 We consider 1 to be a power of a prime and a non-prime-power, but not a prime-power.
%C A373676 A run of a sequence (in this case A000961) is an interval of positions at which consecutive terms differ by one.
%C A373676 The last element of the same run is A373677.
%C A373676 Consists of 1 and all non-prime-powers k such that k-1 is a power of a prime.
%H A373676 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373676 The maximal runs of non-prime-powers begin:
%e A373676    1
%e A373676    6
%e A373676   10
%e A373676   12
%e A373676   14  15
%e A373676   18
%e A373676   20  21  22
%e A373676   24
%e A373676   26
%e A373676   28
%e A373676   30
%e A373676   33  34  35  36
%e A373676   38  39  40
%e A373676   42
%e A373676   44  45  46
%e A373676   48
%e A373676   50  51  52
%e A373676   54  55  56  57  58
%e A373676   60
%t A373676 Select[Range[100],#==1||!PrimePowerQ[#]&&PrimePowerQ[#-1]&]
%Y A373676 See link for prime, composite, squarefree, and nonsquarefree runs/antiruns.
%Y A373676 For runs of powers of primes:
%Y A373676 - length A174965
%Y A373676 - min A373673
%Y A373676 - max A373674
%Y A373676 - sum A373675
%Y A373676 For runs of non-prime-powers:
%Y A373676 - length A110969 (firsts A373669, sorted A373670)
%Y A373676 - min A373676 (this sequence)
%Y A373676 - max A373677
%Y A373676 - sum A373678
%Y A373676 For antiruns of prime-powers:
%Y A373676 - length A373671
%Y A373676 - min A120430
%Y A373676 - max A006549
%Y A373676 - sum A373576
%Y A373676 For antiruns of non-prime-powers:
%Y A373676 - length A373672
%Y A373676 - min A373575
%Y A373676 - max A255346
%Y A373676 - sum A373679
%Y A373676 A000961 lists all powers of primes. A246655 is just prime-powers so lacks 1.
%Y A373676 A025528 counts prime-powers up to n.
%Y A373676 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373676 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A373676 Cf. A000040, A007674, A014963, A038664, A053806, A054265, A068781, A072284, A073051, A373400.
%K A373676 nonn
%O A373676 1,2
%A A373676 _Gus Wiseman_, Jun 16 2024