A373679 - OEIS

%I #6 Jun 17 2024 22:44:14

%S 43,53,21,163,34,35,74,39,126,45,144,51,106,55,56,57,180,128,134,69,

%T 216,75,76,77,324,85,86,87,178,91,92,93,94,95,194,99,306,105,324,111,

%U 226,115,116,117,118,119,242,123,379,262,133,134,135,414,141,142,143

%N Sums of maximal antiruns of non-prime-powers.

%C An antirun of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by more than one.

%H Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.

%e The maximal antiruns of non-prime-powers begin:

%e    1   6  10  12  14

%e   15  18  20

%e   21

%e   22  24  26  28  30  33

%e   34

%e   35

%e   36  38

%e   39

%e   40  42  44

%e   45

%e   46  48  50

%e   51

%e   52  54

%e   55

%e   56

%e   57

%e   58  60  62

%e   63  65

%t Total/@Split[Select[Range[100],!PrimePowerQ[#]&],#1+1!=#2&]//Most

%Y See link for composite, prime, nonsquarefree, and squarefree runs/antiruns.

%Y Prime-power runs: A373675, min A373673, max A373674, length A174965.

%Y Non-prime-power runs: A373678, min A373676, max A373677, length A110969.

%Y Prime-power antiruns: A373576, min A120430, max A006549, length A373671.

%Y Non-prime-power antiruns: A373679 (this sequence), min A373575, max A255346, length A373672.

%Y A000040 lists the primes, differences A001223.

%Y A000961 lists all powers of primes. A246655 lists just prime-powers.

%Y A025528 counts prime-powers up to n.

%Y A057820 gives first differences of consecutive prime-powers, gaps A093555.

%Y A356068 counts non-prime-powers up to n.

%Y A361102 lists all non-prime-powers (A024619 if not including 1).

%Y Cf. A001359, A014963, A027833, A029707, A038664, A054265, A067774, A071148, A251092, A371201, A373401, A373669.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 17 2024