OFFSET
0,3
COMMENTS
A number of the form a(n) + a(n+1) + ... + a(n+k) is never prime for all n, k>=0. It could be proved by the method indicated in the comment in A256581. - Vladimir Shevelev and Peter J. C. Moses, Apr 04 2015
A generalization. Using modified Lengyel's 2007 ideas one can prove that, for every odd r>=3, every number of the form n^r + (n+1)^r + ... + (n+k)^r is nonprime. - Vladimir Shevelev, Apr 04 2015
Composition of the cubes with themselves. - Wesley Ivan Hurt, Apr 01 2016
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000 (first 1000 terms from T. D. Noe)
T. Lengyel, On divisibility of some power sums, INTEGERS, 7(2007), A41, 1-6.
K. MacMillan and J. Sondow, Divisibility of power sums and the generalized Erdős-Moser equation, arXiv:1010.2275 [math.NT], 2010-2011.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
Multiplicative with a(p^e) = p^(9e). - David W. Wilson, Aug 01 2001
Totally multiplicative sequence with a(p) = p^9 for primes p. - Jaroslav Krizek, Nov 01 2009
G.f.: x*(1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8)/(x-1)^10. - R. J. Mathar, Jan 07 2011
a(n) = A000578(n)^3. - Wesley Ivan Hurt, Apr 01 2016
From Amiram Eldar, Oct 08 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(9) (A013667).
Sum_{n>=1} (-1)^(n+1)/a(n) = 255*zeta(9)/256. (End)
MAPLE
MATHEMATICA
Table[n^9, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
Range[0, 30]^9 (* Wesley Ivan Hurt, Apr 01 2016 *)
PROG
(PARI) vector(100, n, (n-1)^9) \\ Derek Orr, Aug 03 2014
(Magma) [n^9 : n in [0..40]]; // Wesley Ivan Hurt, Apr 01 2016
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Sep 19 2000
STATUS
approved