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A117622
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Minesweeper sequence: a(n) is the first nonprime number, k, not occurring previously in the sequence nor the absolute value of its first forward difference among the first differences and a(1)=1.
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2
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1, 4, 6, 10, 9, 14, 8, 15, 24, 12, 20, 30, 16, 27, 40, 18, 33, 49, 21, 38, 56, 22, 42, 63, 25, 44, 68, 26, 51, 28, 54, 81, 32, 62, 91, 34, 65, 98, 35, 70, 102, 36, 72, 111, 39, 76, 116, 45, 86, 129, 46, 90, 135, 48, 94, 141, 50, 100, 52, 104, 155, 55, 108, 162, 57, 112, 168
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Let there be mines under prime numbers in the sequence of natural numbers (on the number line). A man starts from 1 and moves on the line to cover all composite numbers once. He can take a jump of length k only once for every k. He can jump to either side. He moves so that he gives priority to touch the smallest composite number not covered earlier.
Does every composite number get touched?
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EXAMPLE
| Beginning with 1 he takes a jump of 3 to touch 4 then a jump of 2 to touch 6, then a jump of 4 to touch 10 then a jump of 1 in the other direction to touch 9 and so on.
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MATHEMATICA
| f[s_] := Block[{k = 2, d = Abs[Most@s - Rest@s], l = Last@s}, While[ PrimeQ[k] || MemberQ[s, k] || MemberQ[d, Abs[l - k]], k++ ]; Append[s, k]]; Nest[f, {1}, 66] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A117623 (values of k), A081145 (if nothing is mined).
Sequence in context: A028279 A114743 A089546 * A188673 A193951 A129854
Adjacent sequences: A117619 A117620 A117621 * A117623 A117624 A117625
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 08 2006
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EXTENSIONS
| Edited and corrected by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 13 2006
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