OFFSET
1,1
COMMENTS
The computation of integers n such that A256832(n) is not divisible by n, leads to A213891. This sequence contains A213891 as a subsequence.
It appears that 9 is the only composite number in this sequence.
No composites below 10^7. - Charles R Greathouse IV, Apr 20 2016
No composites below 2*10^7. - Charles R Greathouse IV, May 06 2016
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
7 is a term because 1*2*5*12*29*169 = 588120 is not divisible by 7.
MATHEMATICA
With[{s = Sqrt@ 2}, Select[Range[2, 90], ! Divisible[Product[Expand[((1 + s)^k - (1 - s)^k)/2 s], {k, #}]/Simplify[((1 + s)^(# - 1) - (1 - s)^(# -
1))/(2 s)], #] &]] (* Michael De Vlieger, Mar 24 2016, after Vaclav Kotesovec at A256832 and Michael Somos at A000129 *)
PROG
(PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
t(n) = Mod((prod(k=1, n, a000129(k)) / a000129(n-1)), n);
for(n=2, 1e3, if(lift(t(n)) != 0, print1(n, ", ")));
(PARI) is(n)=my(a, b=Mod(1, n), t=b); for(k=2, n-2, [a, b]=[b, a+2*b]; t*=b; if(t==0, return(0))); t*(2*a+5*b) && n>2 \\ Charles R Greathouse IV, Mar 24 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 23 2016
STATUS
approved