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An antirun of a sequence (in this case A005117) is an interval of positions such that at which consecutive terms differ by more than one.
Sum of the n-th maximal antirun of composite numbers differing by more than one.
An antirun of a sequence (in this case A005117) is an interval of positions such that consecutive terms differ by more than one.
Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
allocated for Gus WisemanSum of the n-th antirun of composite numbers differing by more than one.
18, 9, 36, 15, 54, 21, 46, 25, 26, 27, 90, 33, 34, 35, 74, 39, 126, 45, 94, 49, 50, 51, 106, 55, 56, 57, 180, 63, 64, 65, 134, 69, 216, 75, 76, 77, 158, 81, 166, 85, 86, 87, 178, 91, 92, 93, 94, 95, 194, 99, 306, 105, 324, 111, 226, 115, 116, 117, 118, 119
1,1
The length of this antirun is given by A373403.
Row sums of:
4 6 8
9
10 12 14
15
16 18 20
21
22 24
25
26
27
28 30 32
33
34
35
36 38
39
40 42 44
Total/@Split[Select[Range[100], CompositeQ], #1+1!=#2&]//Most
The partial sums are a subset of A053767 (partial sums of composite numbers).
Functional neighbors: A005381, A054265, A068780, A373403, A373405, A373411, A373412.
A000040 lists the primes, differences A001223.
A046933 counts composite numbers between primes.
A065855 counts composite numbers up to n.
Cf. A003114, `A005117, `A025157, A027833, ~A029707, A038664, `A071148, ~A073051, `A110969, ~A174965, A293697, A350842 (strict A350844), A371201.
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Gus Wiseman, Jun 05 2024
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editing
allocated for Gus Wiseman
allocated
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