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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Simon S. Gurvets

Simon S. Gurvets's wiki page.

Simon S. Gurvets has authored 2 sequences.

A343540 Squares visited by a trapped knight on a square-spiral numbered board where the knight is shifted one square up and one square to the right after each move.

Original entry on oeis.org

1, 10, 7, 6, 5, 4, 3, 12, 13, 8, 9, 44, 45, 42, 41, 40, 39, 18, 17, 16, 15, 14, 11, 26, 27, 28, 29, 30, 31, 34, 33, 32, 35, 62, 61, 38, 37, 64, 63, 98, 97, 96, 95, 94, 93, 56, 53, 50, 47, 114, 73, 154, 109, 108, 107, 106, 105, 104, 103, 102
Offset: 1

Views

Author

Simon S. Gurvets, Apr 18 2021

Keywords

Comments

The squares are numbered starting with 1 at the origin (0,0). The sequence is finite: when arriving on square number a(180) = 157, there is no free square within reach for the next move.
Shifting the knight only 1 square to the right leads to an infinite sequence. Similarly, shifting only 1 square up leads to an infinite sequence. More generally, if the knight jumps (1,n) spaces and is shifted m squares to the right, m > n leads to an infinite sequence.

Links

A330008 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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Simon S. Gurvets, Nov 26 2019

Keywords

Comments

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

Links

  • Simon S. Gurvets, Table of n, a(n) for n = 1..209
  • N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).
  • 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.

Crossrefs

Cf. A316667.

Programs

  • 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<A330008=[t+1|t<-A[^-1]] \\ M. F. Hasler, Jan 26 2020

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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