login
This site is supported by donations 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

Table of n, a(n) for n=1..38.

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

Adjacent sequences:  A136582 A136583 A136584 * A136586 A136587 A136588

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 22:18 EDT 2019. Contains 325269 sequences. (Running on oeis4.)