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!)
A083945 Least integer coefficients of A(x), where 1<=a(n)<=5, such that A(x)^(1/5) consists entirely of integer coefficients. 11

%I #12 Oct 31 2013 12:17:23

%S 1,5,5,5,5,1,5,5,5,5,4,5,5,5,5,3,5,5,5,5,2,5,5,5,5,4,5,5,5,5,4,5,5,5,

%T 5,2,5,5,5,5,1,5,5,5,5,5,5,5,5,5,2,5,5,5,5,1,5,5,5,5,5,5,5,5,5,1,5,5,

%U 5,5,3,5,5,5,5,2,5,5,5,5,5,5,5,5,5,3,5,5,5,5,4,5,5,5,5,4,5,5,5,5,5,5,5,5,5

%N Least integer coefficients of A(x), where 1<=a(n)<=5, such that A(x)^(1/5) consists entirely of integer coefficients.

%C More generally, "least integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Is this sequence periodic?

%H Robert G. Wilson v, <a href="/A083945/b083945.txt">Table of n, a(n) for n = 0..3000</a>.

%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

%t a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/5), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* _Robert G. Wilson v_ *)

%Y Cf. A083952, A083953, A083954, A083946.

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 09 2003

%E More terms from _Robert G. Wilson v_, Jul 26 2005

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 March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)