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A373401
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Least k such that the k-th maximal antirun of prime numbers > 3 has length n. Position of first appearance of n in A027833. The sequence ends if no such antirun exists.
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16
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1, 2, 4, 6, 10, 8, 69, 40, 24, 46, 41, 21, 140, 82, 131, 210, 50, 199, 35, 30, 248, 192, 277, 185, 458, 1053, 251, 325, 271, 645, 748, 815, 811, 1629, 987, 826, 1967, 423, 1456, 2946, 1109, 406, 1870, 1590, 3681, 2920, 3564, 6423, 1426, 5953, 8345, 12687, 6846
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OFFSET
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1,2
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COMMENTS
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For this sequence, we define an antirun to be an interval of positions at which consecutive primes differ by at least 3.
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LINKS
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EXAMPLE
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The maximal antiruns of prime numbers > 3 begin:
5
7 11
13 17
19 23 29
31 37 41
43 47 53 59
61 67 71
73 79 83 89 97 101
103 107
109 113 127 131 137
139 149
151 157 163 167 173 179
The a(n)-th rows are:
5
7 11
19 23 29
43 47 53 59
109 113 127 131 137
73 79 83 89 97 101
2269 2273 2281 2287 2293 2297 2309
1093 1097 1103 1109 1117 1123 1129 1151
463 467 479 487 491 499 503 509 521
For example, (19, 23, 29) is the first maximal antirun of length 3, so a(3) = 4.
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MATHEMATICA
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t=Length/@Split[Select[Range[4, 100000], PrimeQ], #1+2!=#2&]//Most;
spna[y_]:=Max@@Select[Range[Length[y]], SubsetQ[t, Range[#]]&];
Table[Position[t, k][[1, 1]], {k, spna[t]}]
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CROSSREFS
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For composite instead of prime we have A073051.
For runs instead of antiruns we have the triple (4,2,1), firsts of A251092.
A046933 counts composite numbers between primes.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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