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%I A270834 #26 May 06 2016 00:18:19
%S A270834 3,7,9,11,19,23,31,43,47,67,71,83,107,127,131,139,151,163,167,191,211,
%T A270834 263,271,283,307,311,331,347,359,367,383,431,439,463,467,479,491,499,
%U A270834 503,523,547,563,571,587,619,631,647,659,691,719,727,739,743,787,811,823,839,859,863,883,887
%N A270834 Numbers n such that A256832(n)/A000129(n-1) is not divisible by n.
%C A270834 The computation of integers n such that A256832(n) is not divisible by n, leads to A213891. This sequence contains A213891 as a subsequence.
%C A270834 It appears that 9 is the only composite number in this sequence.
%C A270834 No composites below 10^7. - _Charles R Greathouse IV_, Apr 20 2016
%C A270834 No composites below 2*10^7. - _Charles R Greathouse IV_, May 06 2016
%H A270834 Charles R Greathouse IV, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EyNzA4MzQvYjI3MDgzNC50eHQ">Table of n, a(n) for n = 1..10000</a>
%e A270834 7 is a term because 1*2*5*12*29*169 = 588120 is not divisible by 7.
%t A270834 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)^(# -
%t A270834 1))/(2 s)], #] &]] (* _Michael De Vlieger_, Mar 24 2016, after _Vaclav Kotesovec_ at A256832 and _Michael Somos_ at A000129 *)
%o A270834 (PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
%o A270834 t(n) = Mod((prod(k=1, n, a000129(k)) / a000129(n-1)), n);
%o A270834 for(n=2, 1e3, if(lift(t(n)) != 0, print1(n, ", ")));
%o A270834 (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
%Y A270834 Cf. A000129, A213891, A256832, A270617.
%K A270834 nonn
%O A270834 1,1
%A A270834 _Altug Alkan_, Mar 23 2016

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