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

1,1

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

Cf. A000129, A213891, A256832, A270617.

Sequence in context: A112398 A197504 A167800 * A192628 A336655 A003538

Adjacent sequences: A270831 A270832 A270833 * A270835 A270836 A270837

Keyword

nonn

Author

Altug Alkan, Mar 23 2016

Status

approved