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A330008
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Squares visited by a knight moving on a square-spiral numbered board where the knight moves to an unvisited square with the lowest prime spiral number, or lowest composite number if no primes are available.
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7
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1, 10, 3, 6, 17, 4, 7, 2, 5, 8, 11, 14, 29, 32, 61, 16, 19, 22, 41, 18, 37, 62, 139, 60, 13, 28, 9, 12, 31, 54, 89, 30, 53, 26, 47, 76, 23, 20, 43, 70, 109, 42, 73, 44, 71, 40, 67, 36, 97, 34, 59, 56, 131, 88, 127, 52, 83, 80, 167, 82, 173, 84, 27, 24, 79, 46, 21, 72, 107
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refs;
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history;
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OFFSET
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1,2
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COMMENTS
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The squares are numbered starting with 1 at the origin (0,0). The sequence is finite: when arriving on square number a(209) = 147, there is no free square within reach for the next move. - M. F. Hasler, Jan 26 2020
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LINKS
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Scott R. Shannon, Image showing the steps of the knight's path. A green dot marks the starting 1 square and a red dot the final square with number 147. The red dot is surrounded by eight blue dots to show the occupied neighboring squares. A yellow dots marks the smallest unvisited square with number 15. Purple dots mark the visited squares containing a prime number. The path after square 1 contains 67 primes and 141 composites.
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PROG
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(PARI) local(U); my(v(p)=if(bittest(U, p), [9, 0], [1-isprime(p+1), p]), nxt(x)=vecsort([v(pos(x+k))|k<-K])[1][2], K=[[(-1)^(i\2)<<(i>4), (-1)^i<<(i<5)]|i<-[1..8]], pos(x, y=x[2])=if(y>=abs(x=x[1]), 4*y^2-y-x, -x>=abs(y), 4*x^2-x-y, -y>=abs(x), (4*y-3)*y+x, (4*x-3)*x+y), xy(n, m=sqrtint(n), k=m\/2)=if(m<=n-=4*k^2, [n-3*k, -k], n>=0, [-k, k-n], n>=-m, [-k-n, k], [k, 3*k+n]), A=List(0)); until(!listput(A, nxt(xy(A[#A]))), U+=1<<A[#A]); A330008=[t+1|t<-A[^-1]] \\ M. F. Hasler, Jan 26 2020
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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