

A309816


a(n) is the 2adic valuation of A014664(n).


0



1, 2, 0, 1, 2, 3, 1, 0, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 0, 0, 0, 1, 0, 4, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 2, 1, 0, 2, 1, 2, 0, 5, 2, 0, 1, 0, 1, 2, 0, 0, 3, 1, 4, 0, 2, 0, 2, 1, 1, 2, 1, 0, 2, 2, 1, 0, 1, 2, 3, 0, 0, 2, 1, 0, 2, 2, 3, 2, 1, 2, 0, 3, 0, 1, 5, 2
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OFFSET

2,2


COMMENTS

Let p and q be distinct odd primes. Then there exists an integer i such that 2^i == 1 (mod p*q) if and only if a(u) = a(v) and a(u), a(v) > 0, where u and v are the indices of p and q in A000040, respectively (cf. Anderson, Preece, 2008, Lemma 1.4).


LINKS

Table of n, a(n) for n=2..88.
I. Anderson and D. A. Preece, A general approach to constructing powersequence terraces for Z_n, Discrete Mathematics, Vol. 308, No. 56 (2008), 631644.


EXAMPLE

For n = 7: A014664(7) = 8 and the 2adic valuation of 8 is 3, since 2^3 = 8, so a(7) = 3.


PROG

(PARI) a014664(n) = my(p=prime(n)); znorder(Mod(2, p))
a(n) = valuation(a014664(n), 2)


CROSSREFS

Cf. A000040, A014664.
Sequence in context: A117398 A295989 A240852 * A071486 A046695 A071433
Adjacent sequences: A309813 A309814 A309815 * A309817 A309818 A309819


KEYWORD

nonn,easy


AUTHOR

Felix FrÃ¶hlich, Aug 18 2019


STATUS

approved



