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A373669
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Least k such that the k-th maximal run of non-prime-powers has length n. Position of first appearance of n in A110969, and the sequence ends if there is none.
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11
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1, 5, 7, 12, 18, 190, 28, 109, 40, 28195574, 53
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OFFSET
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1,2
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COMMENTS
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A run of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by one.
Are there only 9 terms?
No. a(10) exists.
Between the prime 144115188075855859 and 144115188075855872 = 2^57 there are 12 non-prime-powers so a(12) exists. (End)
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LINKS
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EXAMPLE
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The maximal runs of non-prime-powers begin:
1
6
10
12
14 15
18
20 21 22
24
26
28
30
33 34 35 36
38 39 40
42
44 45 46
48
50 51 52
54 55 56 57 58
60
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MATHEMATICA
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q=Length/@Split[Select[Range[10000], !PrimePowerQ[#]&], #1+1==#2&]//Most;
spna[y_]:=Max@@Select[Range[Length[y]], SubsetQ[y, Range[#1]]&];
Table[Position[q, k][[1, 1]], {k, spna[q]}]
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CROSSREFS
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For squarefree runs we have firsts of A120992.
For prime-powers runs we have firsts of A174965.
For antiruns we have firsts of A373672.
For runs of non-prime-powers:
A000961 lists the powers of primes (including 1).
A057820 gives first differences of consecutive prime-powers, gaps A093555.
Cf. A007053, A008864, A014963, A027833, A038664, A054265, A067774, A356068, A373401, A373403, A373671.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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