

A053447


Multiplicative order of 4 mod 2n+1.


21



1, 1, 2, 3, 3, 5, 6, 2, 4, 9, 3, 11, 10, 9, 14, 5, 5, 6, 18, 6, 10, 7, 6, 23, 21, 4, 26, 10, 9, 29, 30, 3, 6, 33, 11, 35, 9, 10, 15, 39, 27, 41, 4, 14, 11, 6, 5, 18, 24, 15, 50, 51, 6, 53, 18, 18, 14, 22, 6, 12, 55, 10, 50, 7, 7, 65, 9, 18, 34, 69, 23, 30, 14, 21, 74, 15, 12, 10, 26
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OFFSET

0,3


COMMENTS

For a set S = {x, y} (x < y), let f(S) = {2x, y  x}, then a(n) is the smallest k > 0 such that f_k({1, 2n}) = {1, 2n} where f_k(S) denotes iteration for k times. E.g., for n = 3 we have: f_1({1, 6}) = f({1, 6}) = {2, 5}, f_2({1, 6}) = f({2, 5}) = {3, 4}, f_3({1, 6}) = f({3, 4}) = {1, 6}.  Jianing Song, Jan 27 2019


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Multiplicative Order


FORMULA

Let b = A002326, then a(n) = b(n) if b(n) is odd, otherwise a(n) = b(n)/2.  Joerg Arndt, Feb 03 2019


MATHEMATICA

Table[ MultiplicativeOrder[4, n], {n, 1, 160, 2}] (* Robert G. Wilson v, Apr 05 2011 *)


PROG

(Magma) [1] cat [Modorder(4, 2*n+1): n in [1..100]]; // Vincenzo Librandi, Apr 01 2014
(PARI) a(n) = znorder(Mod(4, 2*n+1)); \\ Michel Marcus, Feb 05 2015
(GAP) List([0..80], n>OrderMod(4, 2*n+1)); # Muniru A Asiru, Feb 25 2019


CROSSREFS

Cf. A070667A070675, A002326, A070676, A070677, A070681, A070678, A053451, A070679, A070682, A070680, A070683, A302141.
Sequence in context: A212792 A281363 A050976 * A185026 A289630 A023160
Adjacent sequences: A053444 A053445 A053446 * A053448 A053449 A053450


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



