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A270834 Numbers n such that A256832(n)/A000129(n-1) is not divisible by n. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A003538 A018596

Adjacent sequences:  A270831 A270832 A270833 * A270835 A270836 A270837

KEYWORD

nonn

AUTHOR

Altug Alkan, Mar 23 2016

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)