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A275335
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The primes in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.
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2
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1, 2, 4, 3, 5, 6, 7, 11, 13, 17, 8, 9, 10, 12, 14, 15, 16, 18, 19, 23, 29, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 37, 41, 43, 47, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 59, 61, 67, 71, 73, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 83, 89, 97, 101, 103, 107, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 110, 111
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OFFSET
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1,2
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COMMENTS
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This is the lexicographically first such sequence starting with a(1)=1 and being always extended with the smallest integer not yet present that doesn't lead to a contradiction.
The sequence is a permutation of the integers > 0.
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LINKS
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EXAMPLE
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The blocks of primes are indicated here by parentheses; the successive block-sizes are 1, 2, 4, 3, 5,... which reproduces the sequence itself:
1,(2),4,(3,5),6,(7,11,13,17),8,9,10,12,14,15,16,18,(19,23,29),20,21,22,24,25,26,27,28,30,(31,37,41,43,47),32,33,.
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MATHEMATICA
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a = {1}; b = 1; c = Select[Range[10^4], CompositeQ]; Do[k = b + a[[i]] - 1; a = Join[a, Join[Prime@ Range[b, k], If[Prime@ b == 2, {4}, TakeWhile[c, # < NextPrime@ Prime@ k &] ] ]]; c = DeleteCases[c, k_ /; k <= Last@ a]; b = k + 1, {i, 8}]; a (* Michael De Vlieger, Jul 25 2016 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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