_T. D. Noe (noe(AT)sspectra.com), _, Aug 17 2002
_T. D. Noe (noe(AT)sspectra.com), _, Aug 17 2002
proposed
approved
The first 51 terms are given. a(n) > 0 for n=52, 53, and 56, and a(n) = 0 for n=54, 55, and 57. It is known that a(n) > 0 for 58 <= n <=59-66,71,73-79,81,84,87-96 and 98- 200. It is conjectured that a(n) > 0 for all n > 9757. A greedy algorithm can be used to quickly find a solution for many n. See the link to puzzle 189 for more details. The Mathematica program uses a backtracking algorithm to count the arrangements. To print the unique arrangements, remove the comments from around the print statement.
approved
proposed
The first 51 terms are given. It is known that a(n) > 0 for n=59-66,71,73-79,81,84,87-96, and 98-200. It is conjectured that a(n) > 0 for all n > 97. A greedy algorithm can be used to quickly find a solution for many n. See the link to puzzle 189 for more details. The Mathematica program uses a backtracking algorithm to count the arrangements. To print the unique arrangements, remove the comments from around the print statement.
hard,more,nice,nonn,new
nMax=12; $RecursionLimit=500; try[lev_] := Module[{t, j, circular}, If[lev>n, circular=PrimeQ[soln[[1]]^2+soln[[n]]^2]&&PrimeQ[soln[[1]]+soln[[n]]]; If[(!circular&&soln[[1]]<soln[[n]])||(circular&&soln[[1]]==1&&soln[[2]]<=soln[[n
hard,more,nice,nonn,new
nMax=12; $RecursionLimit=500; try[lev_] := Module[{t, j, circular}, If[lev>n, circular=PrimeQ[soln[[1]]^2+soln[[n]]^2]&&PrimeQ[soln[[1]]+soln[[n]]]; If[(!circular&&soln[[1]]<soln[[n]])||(circular&&soln[[1]]==1&&soln[[2]]<=soln[[n
hard,more,nice,nonn,new
nMax=12; $RecursionLimit=500; try[lev_]:=Module[{t, j, circular}, If[lev>n, circular=PrimeQ[soln[[1]]^2+soln[[n]]^2]&&PrimeQ[soln[[1]]+soln[[n]]]; If[(!circular&&soln[[1]]<soln[[n]])||(circular&&soln[[1]]==1&&soln[[2]]<=soln[[n
hard,more,nice,nonn,new
a(n) is the number of essentially different ways in which the integers 1,2,3,...,n can be arranged in a sequence such that (1) adjacent integers sum to a prime number and (2) squares of adjacent numbers sum to a prime number. Rotations and reversals are counted only once.
1, 1, 1, 1, 0, 1, 0, 0, 0, 3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
1,10
The first 51 terms are given. It is known that a(n) > 0 for n=59-66,71,73-79,81,84,87-96, and 98-200. It is conjectured that a(n) > 0 for all n > 97. A greedy algorithm can be used to quickly find a solution for many n. See the link to puzzle 189 for more details. The Mathematica program uses a backtracking algorithm to count the arrangements. To print the unique arrangements, remove the comments from around the print statement.
Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_189.htm">Puzzle 189: Squares and primes in a row</a>
a(4)=1 because there is essentially one arrangement: {3,2,1,4}.
nMax=12; $RecursionLimit=500; try[lev_]:=Module[{t, j, circular}, If[lev>n, circular=PrimeQ[soln[[1]]^2+soln[[n]]^2]&&PrimeQ[soln[[1]]+soln[[n]]]; If[(!circular&&soln[[1]]<soln[[n]])||(circular&&soln[[1]]==1&&soln[[2]]<=soln[[n
hard,more,nice,nonn
T. D. Noe (noe(AT)sspectra.com), Aug 17 2002
approved