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 A073451 Number of essentially different ways in which the squares 1,4,9,...,n^2 can be arranged in a sequence such that all pairs of adjacent squares sum to a prime number. Rotations and reversals are counted only once. 3
 1, 1, 1, 1, 2, 4, 0, 12, 6, 66, 156, 44, 312, 1484, 2672, 6680, 19080, 45024, 168496, 2033271, 724543, 2776536, 24598062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Note that when the first and last numbers of an arrangement sum to a prime, then there are n rotations that are treated as one arrangement. The case n=10 exhibits the first of these rotational solutions: {1,4,9,64,49,100,81,16,25,36}. The Mathematica program uses a backtracking algorithm to count the arrangements. To print the unique arrangements, remove the comments from around the print statement. LINKS Carlos Rivera, Puzzle 189: Squares and primes in a row EXAMPLE a(5)=2 because there are two essential different arrangements: {9,4,1,16,25} and {9,4,25,16,1}. MATHEMATICA nMax=12; \$RecursionLimit=500; try[lev_] := Module[{t, j, circular}, If[lev>n, circular=PrimeQ[soln[[1]]^2+soln[[n]]^2]; If[(!circular&&soln[[1]]

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)