cp's OEIS Frontend

A373677 Last element of each maximal run of non-prime-powers.

%I A373677 #8 Jun 17 2024 14:48:39
%S A373677 1,6,10,12,15,18,22,24,26,28,30,36,40,42,46,48,52,58,60,63,66,70,72,
%T A373677 78,80,82,88,96,100,102,106,108,112,120,124,126,130,136,138,148,150,
%U A373677 156,162,166,168,172,178,180,190,192,196,198,210,222,226,228,232,238
%N A373677 Last element of each maximal run of non-prime-powers.
%C A373677 We consider 1 to be a power of a prime and a non-prime-power, but not a prime-power.
%C A373677 A run of a sequence (in this case A000961) is an interval of positions at which consecutive terms differ by one.
%C A373677 The first element of the same run is A373676.
%C A373677 Consists of all non-prime-powers k such that k+1 is a prime-power.
%H A373677 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373677 The maximal runs of non-prime-powers begin:
%e A373677    1
%e A373677    6
%e A373677   10
%e A373677   12
%e A373677   14  15
%e A373677   18
%e A373677   20  21  22
%e A373677   24
%e A373677   26
%e A373677   28
%e A373677   30
%e A373677   33  34  35  36
%e A373677   38  39  40
%e A373677   42
%e A373677   44  45  46
%e A373677   48
%e A373677   50  51  52
%e A373677   54  55  56  57  58
%e A373677   60
%t A373677 Select[Range[100],!PrimePowerQ[#]&&PrimePowerQ[#+1]&]
%Y A373677 See link for prime, composite, squarefree, and nonsquarefree runs/antiruns.
%Y A373677 For runs of powers of primes:
%Y A373677 - length A174965
%Y A373677 - min A373673
%Y A373677 - max A373674
%Y A373677 - sum A373675
%Y A373677 For runs of non-prime-powers:
%Y A373677 - length A110969 (firsts A373669, sorted A373670)
%Y A373677 - min A373676
%Y A373677 - max A373677 (this sequence)
%Y A373677 - sum A373678
%Y A373677 For antiruns of prime-powers:
%Y A373677 - length A373671
%Y A373677 - min A120430
%Y A373677 - max A006549
%Y A373677 - sum A373576
%Y A373677 For antiruns of non-prime-powers:
%Y A373677 - length A373672
%Y A373677 - min A373575
%Y A373677 - max A255346
%Y A373677 - sum A373679
%Y A373677 A000961 lists all powers of primes. A246655 is just prime-powers so lacks 1.
%Y A373677 A025528 counts prime-powers up to n.
%Y A373677 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A373677 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A373677 Cf. A000040, A005381, A007674, A014963, A038664, A068780, A068781, A073051, A373400, A373401.
%K A373677 nonn
%O A373677 1,2
%A A373677 _Gus Wiseman_, Jun 16 2024