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 A136585 Solutions of an a*x+b*y=c Prime Diophantine Equation: Prime[m]x+Prime[m+1]*y=Prime[m-1] : as Abs[n*Prime[m]] Or Abs[n*Prime[m+1]] in x+y*n=Prime[m-1]. 0
 2, 4, 5, 6, 9, 20, 33, 35, 42, 44, 57, 68, 104, 114, 117, 119, 145, 174, 279, 301, 310, 322, 345, 376, 410, 430, 517, 533, 590, 649, 740, 777, 976, 1159, 1537, 1590, 2345, 2412 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Starting at the second prime 3, solutions are obtained to the Equation x+y*n=Prime[m-1] or n=(Prime[m-1]+x)/y Either n*Prime[m]/or n*Prime[m+1] is an Integer. using the Wagon Diophantine solver Module for n and then the specific prime that it is a rational number of is multiplied out to give an Integer. The resulting numbers are made positive and sorted for magnitude to give the output sequence. This sequence is an effort to get some sequence related by the primes: {Prime[m-1],Prime[m],Prime[m+1]} by Prime[m]x+Prime[m+1]*y=Prime[m-1] REFERENCES A Course in Computational Number Theory by Bressoud and Wagon,2001 LINKS FORMULA a[out]=Abs[If[ IntegerQ[n*Prime[m+1]],n*Prime[m+1] else n*Prime[m]]] where n is a rational number: n=(Prime[m-1]+x)/y Sequence is sorted by magnitude. MATHEMATICA Clear[n, m, l] DiophantineSolve[{a_, b_}, c_, n_] := Module[{d, e}, {d, e} = ExtendedGCD[a, b]; If[Mod[c, d] == 0, Transpose[{c*e, {b, -a}}/d].{1, n}, {}]]; a = Table[Table[Simplify[If[l == 2, Prime[m], Prime[m + 1]]*(n /. Solve[DiophantineSolve[{Prime[m], Prime[m + 1]}, Prime[m - 1], n][[l]] - Prime[m - 1] == 0, n])], {l, 2, 1, -1}], {m, 2, 20}]; Union[Abs[Flatten[a]]] CROSSREFS Sequence in context: A056635 A163116 A003306 * A122721 A014224 A175342 Adjacent sequences:  A136582 A136583 A136584 * A136586 A136587 A136588 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Mar 26 2008 STATUS approved

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Last modified May 23 05:24 EDT 2013. Contains 225585 sequences.