[seqfan] Re: You wouldn't believe (fwd) A005178
David Wilson
dwilson at gambitcomm.com
Mon Dec 22 23:20:06 CET 2008
By which you mean "A005178 mod 100 is periodic modulo 30"
Every integer sequence with a rational g.f. is a linear recurrence.
Every integer linear recurrence is eventually periodic in every modulus.
My apologies if I missed something special about the values of A005178
mod 100.
Artur wrote:
> Dear Richard and Seqfans,
>
> A005178 is periodic modulo 30 (pay attention that start from 0 not 1):
>
> %C A005178 congruent to 0 mod 100 if n is congruent to 14 or 29 mod 30
> %C A005178 congruent to 1 mod 100 if n is congruent to 0 or 1 or 12 or 16 or 27 or 28 mod 30
> %C A005178 congruent to 5 mod 100 if n is congruent to 2 or 11 or 17 or 26 mod 30
> %C A005178 congruent to 11 mod 100 if n is congruent to 3 or 25 mod 30
> %C A005178 congruent to 36 mod 100 if n is congruent to 4 or 9 or 19 or 24 mod 30
> %C A005178 congruent to 45 mod 100 if n is congruent to 8 or 20 mod 30
> %C A005178 congruent to 51 mod 100 if n is congruent to 13 or 15 mod 30
> %C A005178 congruent to 61 mod 100 if n is congruent to 10 or 18 mod 30
> %C A005178 congruent to 81 mod 100 if n is congruent to 6 or 7 or 21 or 22 mod 30
> %C A005178 congruent to 95 mod 100 if n is congruent to 5 or 23 mod 30
>
> Together 10 different rests modulo 30.
>
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