A270834 Numbers n such that A256832(n)/A000129(n-1) is not divisible by n.

3, 7, 9, 11, 19, 23, 31, 43, 47, 67, 71, 83, 107, 127, 131, 139, 151, 163, 167, 191, 211, 263, 271, 283, 307, 311, 331, 347, 359, 367, 383, 431, 439, 463, 467, 479, 491, 499, 503, 523, 547, 563, 571, 587, 619, 631, 647, 659, 691, 719, 727, 739, 743, 787, 811, 823, 839, 859, 863, 883, 887

Offset: 1

Author

Altug Alkan, Mar 23 2016

Keywords

• nonn

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

Examples

			7 is a term because 1*2*5*12*29*169 = 588120 is not divisible by 7.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000129, A213891, A256832, A270617.

Programs

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 *)

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