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.

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

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

Table of n, a(n) for n=1..67.

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

Adjacent sequences: A117619 A117620 A117621 * A117623 A117624 A117625

Keyword

nonn

Author

Amarnath Murthy, Apr 08 2006

Extensions

Edited and corrected by Robert G. Wilson v, Jun 13 2006

Status

approved