login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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: A163116 A003306 A250305 * A122721 A014224 A175342
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Mar 26 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 21:07 EDT 2023. Contains 363028 sequences. (Running on oeis4.)