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!)
A154333 Difference between n^3 and the next smaller square 6
1, 4, 2, 15, 4, 20, 19, 28, 53, 39, 35, 47, 81, 40, 11, 127, 13, 56, 135, 79, 45, 39, 67, 135, 249, 152, 83, 48, 53, 104, 207, 7, 216, 100, 26, 431, 28, 116, 270, 496, 277, 104, 546, 503, 524, 615, 139, 368, 685, 391, 155, 732, 652, 648, 726, 55, 293, 631, 170, 704, 405 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The sequence A077116(n) = n^3-[sqrt(n^3)]^2 satisfies A077116(n)=0 <=> n^3 is a square <=> n is a square. It differs from the present sequence (which is always positive) only in these indices, where a(k^2)=2k^3-1.
LINKS
FORMULA
a(n) = n^3 - [sqrt(n^3 - 1)]^2 = A000578(n) - A048760(n^3-1). a(k^2) = 2 k^3 - 1.
a(n) = A071797(n^3). - R. J. Mathar, May 29 2016
MAPLE
A154333 := proc(n)
A071797(n^3) ;
end proc: # R. J. Mathar, May 29 2016
MATHEMATICA
nss[n_]:=Module[{n3=n^3, s}, s=Floor[Sqrt[n3]]^2; If[s==n3, s=(Sqrt[s]- 1)^2, s]]; Table[n^3-nss[n], {n, 70}] (* Harvey P. Dale, Jan 19 2017 *)
PROG
(PARI) A154333(n) = n^3-sqrtint(n^3-1)^2
a154333 = vector(90, n, n^3-sqrtint(n^3-1)^2)
CROSSREFS
Cf. A087285 (range of this sequence, excluding the initial term 1).
Sequence in context: A360084 A019061 A019012 * A185130 A261870 A325516
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 07 2009
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 24 21:23 EDT 2024. Contains 372781 sequences. (Running on oeis4.)