The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A053446 Multiplicative order of 3 mod m, where gcd(m, 3) = 1. 17
 1, 1, 2, 4, 6, 2, 4, 5, 3, 6, 4, 16, 18, 4, 5, 11, 20, 3, 6, 28, 30, 8, 16, 12, 18, 18, 4, 8, 42, 10, 11, 23, 42, 20, 6, 52, 20, 6, 28, 29, 10, 30, 16, 12, 22, 16, 12, 35, 12, 18, 18, 30, 78, 4, 8, 41, 16, 42, 10, 88, 6, 22, 23, 36, 48, 42, 20, 100, 34, 6, 52, 53, 27, 20, 12, 112, 44 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Essentially the same as A050975. - R. J. Mathar, Oct 13 2008 Let k, m be any positive numbers not divisible by 3. Let k <+> m denote that of the two numbers k + m, k + 2*m which is divisible by 3. Finally, for a number t divisible by 3, let t* = t/3^s where s is the 3-adic order of t. Let u = u(n) be the n-th number which is not divisible by 3. Consider the following algorithm of the calculating a(n), similar to the algorithm in A002326: Compute successively r_1 = (1 <+> u)*, r_2 = (r_1 <+> u)*, ..., r_h = (r_(h-1) <+> u)* and finish as soon as r_h = 1. Then a(n) = s(1 <+> u) + s(r_1 <+> u) + ... + s(r_(h-1) <+> u). Note that by a similar algorithm one can compute an arbitrary multiplicative order of a mod b, where gcd(a, b) = 1. - Vladimir Shevelev, Oct 06 2017 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = multiplicative order of 3 modulo floor((3*n-1)/2) = A001651(n), for n >= 1. - Wolfdieter Lang, Sep 28 2020 EXAMPLE From Vladimir Shevelev, Oct 06 2017: (Start) 7 is the fifth number not divisible by 3. According to the algorithm in the comment we have in the form of a "finite continued fraction"     1 + 14     ------ + 7        3     ---------- + 14           3     ----------------- + 7             3^2     ---------------------- = 1                3^2 Summing the exponents of 3 in the denominators, we obtain a(5) = 1 + 1 + 2 + 2 = 6. (End) MATHEMATICA MultiplicativeOrder[3, #] & /@ Select[ Range@ 115, GCD[3, #] == 1 &] (* Robert G. Wilson v, Apr 05 2011 *) PROG (PARI) lista(nn) = {for (n=1, nn, if (gcd(n, 3) == 1, print1(znorder(Mod(3, n)), ", ")); ); } \\ Michel Marcus, Feb 06 2015 (Sage) [Mod(3, n).multiplicative_order() for n in (1..115) if gcd(n, 3) == 1] # Peter Luschny, Oct 07 2017 (GAP) List(Filtered([1..130], n->Gcd(n, 3)=1), n->OrderMod(3, n)); # Muniru A Asiru, Feb 26 2019 CROSSREFS Cf. A001651, A002326, A050975. Sequence in context: A075242 A161489 A050975 * A133903 A278263 A236188 Adjacent sequences:  A053443 A053444 A053445 * A053447 A053448 A053449 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)