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%I #7 Dec 05 2013 19:57:14
%S 1,4,6,10,9,14,8,15,24,12,20,30,16,27,40,18,33,49,21,38,56,22,42,63,
%T 25,44,68,26,51,28,54,81,32,62,91,34,65,98,35,70,102,36,72,111,39,76,
%U 116,45,86,129,46,90,135,48,94,141,50,100,52,104,155,55,108,162,57,112,168
%N 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.
%C 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.
%C Does every composite number get touched?
%e 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.
%t 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_ *)
%Y Cf. A117623 (values of k), A081145 (if nothing is mined).
%K nonn
%O 1,2
%A _Amarnath Murthy_, Apr 08 2006
%E Edited and corrected by _Robert G. Wilson v_, Jun 13 2006
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