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A117622 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. 2
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; text; internal format)
OFFSET
1,2
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?
LINKS
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.
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 *)
CROSSREFS
Cf. A117623 (values of k), A081145 (if nothing is mined).
Sequence in context: A363700 A249982 A292767 * A188673 A365448 A193951
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 08 2006
EXTENSIONS
Edited and corrected by Robert G. Wilson v, Jun 13 2006
STATUS
approved

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)