The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A322548 Integers x such that x^2 + 119 = 15*2^y. 0
1, 11, 19, 29, 61, 701 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The exponents y of the corresponding powers of 2 are 3, 4, 5, 6, 8, 15.
The list gives all positive integers x such that x^2 + 119 = 15*2^y.
Yann Bugeaud proposed the problem to prove that there is an absolute constant C such that, for any positive integers D, k and a prime number p such that gcd(D, kp) = 1, the Diophantine equation x^2 + D = k*p^n has at most C integer solutions (x, n) (Problem 9 of the list of 22 open problems below).
LINKS
Jan-Hendrik Evertse, Some open problems about Diophantine equations, 22 problems posed at the Instructional conference and workshop "Solvability of Diophantine equations", May 7-16, 2007, Lorentz Center, Leiden.
Jörg Stiller, The Diophantine equation x^2 + 119 = 15*2^n has exactly six solutions, Rocky Mountain J. Math. 26 (1996), 295-298.
EXAMPLE
a(2) = 11: 11^2 + 119 = 240 = 15*2^4.
MATHEMATICA
s={}; Do[r = Solve[x^2 + 119 == 15*2^k && x >= 0, x, Integers]; If[Length[r]>0, AppendTo[s, x/.r[[1]]]], {k, 1, 15}]; s (* Amiram Eldar, Dec 15 2018 *)
CROSSREFS
Cf. A038198 (All solutions to x^2 + 7 = 2^y).
Sequence in context: A175275 A094517 A196669 * A049719 A155555 A357426
KEYWORD
nonn,fini,full
AUTHOR
Tomohiro Yamada, Dec 14 2018
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 29 04:26 EDT 2024. Contains 372921 sequences. (Running on oeis4.)