A022531 Nexus numbers (n+1)^15 - n^15.

1, 32767, 14316139, 1059392917, 29443836301, 439667406451, 4277376525367, 30436810578889, 170706760005817, 794108867905351, 3177248169415651, 11229773405170717, 35778871439504389, 104382202543721467, 282325794823047151, 715027614225987601, 1709501546902968817

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Nexus Number.

Crossrefs

Column k = 14 of A047969.

Cf. A010803 (n^15).

Programs

Magma

[(n+1)^15-n^15: n in [0..20]]; // Vincenzo Librandi, Nov 22 2011

Maple

b:=15: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # Muniru A Asiru, Feb 28 2018

Mathematica

Table[(n + 1)^15 - n^15, {n, 0, 20}] (* Vincenzo Librandi, Nov 22 2011 *)
#[[2]]-#[[1]]&/@Partition[Range[0,20]^15,2,1] (* Harvey P. Dale, Aug 07 2022 *)

PARI

for(n=0,20, print1((n+1)^15 - n^15, ", ")) \\ G. C. Greubel, Feb 27 2018

Formula

G.f.: ( -1 - 32752*x - 13824739*x^2 - 848090912*x^3 - 15041229521*x^4 - 102776998928*x^5 - 311387598411*x^6 - 447538817472*x^7 - 311387598411*x^8 - 102776998928*x^9 - 15041229521*x^10 - 848090912*x^11 - 13824739*x^12 - 32752*x^13 - x^14 ) / (x - 1)^15. - R. J. Mathar, Sep 02 2016

a(n) = A010803(n+1) - A010803(n). - Michel Marcus, Feb 28 2018

Extensions

More terms added by G. C. Greubel, Feb 27 2018