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!)
A343397 Number of ways to write n as 2^x + [y^2/3] + [z^2/4] with x,y,z positive integers, where [.] is the floor function. 10
0, 1, 2, 3, 4, 4, 5, 5, 8, 5, 9, 5, 8, 8, 6, 9, 9, 10, 8, 11, 10, 10, 9, 9, 14, 8, 8, 10, 12, 11, 6, 14, 13, 10, 12, 13, 15, 11, 13, 9, 20, 6, 12, 17, 13, 13, 10, 11, 17, 12, 11, 13, 15, 14, 9, 13, 13, 14, 11, 18, 11, 15, 7, 12, 22, 13, 14, 17, 17, 11, 15, 13, 24, 16, 9, 17, 15, 15, 14, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Conjecture: a(n) > 0 for all n > 1.
We have verified a(n) > 0 for all n = 2..2*10^6.
Conjecture verified up to 10^10. - Giovanni Resta, Apr 14 2021
LINKS
Zhi-Wei Sun, Natural numbers represented by [x^2/a] + [y^2/b] + [z^2/c], arXiv:1504.01608 [math.NT], 2015.
EXAMPLE
a(2) = 1 with 2 = 2^1 + [1^2/3] + [1^2/4].
a(3) = 2 with 3 = 2^1 + [1^2/3] + [2^2/4] = 2^1 + [2^2/3] + [1^2/4].
MATHEMATICA
PowQ[n_]:=PowQ[n]=n>1&&IntegerQ[Log[2, n]];
tab={}; Do[r=0; Do[If[PowQ[n-Floor[x^2/3]-Floor[y^2/4]], r=r+1], {x, 1, Sqrt[3n-1]}, {y, 1, Sqrt[4(n-Floor[x^2/3]-1)+1]}]; tab=Append[tab, r], {n, 1, 80}]; Print[tab]
CROSSREFS
Sequence in context: A216411 A110532 A049987 * A270832 A257646 A051898
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Apr 13 2021
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 June 20 08:48 EDT 2024. Contains 373515 sequences. (Running on oeis4.)