

A214027


The number of zeros in the fundamental Pisano period of the sequence A000129 mod n.


6



1, 1, 2, 1, 4, 2, 1, 1, 2, 2, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 4, 2, 2, 1, 4, 2, 1, 1, 2, 2, 2, 2, 4, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 4, 2, 2, 1, 2, 2, 2, 2, 4, 1, 2, 1, 4, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1
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OFFSET

1,3


COMMENTS

This is intimately connected with A175181 and A214028, much as A001176 is intimately connected with A001175 and A001177. In fact, A175181(n)/a(n) = A214028(n). This is the same divisibility relation that holds between A001175, A001176 and A001177.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

From Jianing Song, Sep 12 2018: (Start)
For odd primes p, a(p^e) = 4 if A214028(p) is odd; 1 if A214028(p) is even but not divisible by 4; 2 if A214028(p) is divisible by 4.
a(n) = 2 for n == 3 (mod 8). For primes p, a(p^e) = 1 if p == 7 (mod 8), 4 if p == 5 (mod 8). Conjecture: 1/6 of the primes congruent to 1 mod 8 satisfy a(p^e) = 1, 2/3 of them satisfy a(p^e) = 2 and 1/6 of them satisfy a(p^e) = 4.
(End)


MATHEMATICA

Join[{1}, Table[s = t = Mod[{0, 1}, n]; zeros = 0; While[tmp = Mod[2*t[[2]] + t[[1]], n]; t[[1]] = t[[2]]; t[[2]] = tmp; s != t, If[tmp == 0, zeros++]]; zeros, {n, 2, 100}]] (* T. D. Noe, Jul 09 2012 *)


CROSSREFS

Cf. A175181, A214028.
Sequence in context: A244554 A194735 A130544 * A007739 A290935 A031424
Adjacent sequences: A214024 A214025 A214026 * A214028 A214029 A214030


KEYWORD

nonn


AUTHOR

Art DuPre, Jul 04 2012


STATUS

approved



