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A373402
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Numbers k such that the k-th maximal antirun of prime numbers > 3 has length different from all prior maximal antiruns. Sorted list of positions of first appearances in A027833.
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9
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1, 2, 4, 6, 8, 10, 21, 24, 30, 35, 40, 41, 46, 50, 69, 82, 131, 140, 185, 192, 199, 210, 248, 251, 271, 277, 325, 406, 423, 458, 645, 748, 811, 815, 826, 831, 987, 1053, 1109, 1426, 1456, 1590, 1629, 1870, 1967, 2060, 2371, 2607, 2920, 2946, 3564, 3681, 4119
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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 begin:
5
7 11
19 23 29
43 47 53 59
73 79 83 89 97 101
109 113 127 131 137
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MATHEMATICA
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t=Length/@Split[Select[Range[4, 10000], PrimeQ], #1+2!=#2&]//Most;
Select[Range[Length[t]], FreeQ[Take[t, #-1], t[[#]]]&]
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CROSSREFS
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For squarefree runs we have the triple (1,3,5), firsts of A120992.
For prime runs we have the triple (1,2,3), firsts of A175632.
For nonsquarefree runs we have A373199 (assuming sorted), firsts of A053797.
For composite antiruns we have the triple (1,2,7), firsts of A373403.
A046933 counts composite numbers between primes.
A065855 counts composite numbers up to n.
Cf. A006512, A007674, A049093, A068781, A072284, A077641, A174965, A251092, A373198, A373408, A373411.
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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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