

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
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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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



