The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322907 Entry points for the 3-Fibonacci numbers A006190. 10
 1, 3, 2, 6, 3, 6, 8, 6, 6, 3, 4, 6, 13, 24, 6, 12, 8, 6, 20, 6, 8, 12, 22, 6, 15, 39, 18, 24, 7, 6, 32, 24, 4, 24, 24, 6, 19, 60, 26, 6, 7, 24, 42, 12, 6, 66, 48, 12, 56, 15, 8, 78, 26, 18, 12, 24, 20, 21, 12, 6, 30, 96, 24, 48, 39, 12, 68, 24, 22, 24, 72, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the smallest k > 0 such that n divides A006190(k). a(n) is also called the rank of A006190(n) modulo n. For primes p == 1, 9, 17, 25, 29, 49 (mod 52), a(p) divides (p - 1)/2. For primes p == 3, 23, 27, 35, 43, 51 (mod 52), a(p) divides p - 1, but a(p) does not divide (p - 1)/2. For primes p == 5, 21, 33, 37, 41, 45 (mod 52), a(p) divides (p + 1)/2. For primes p == 7, 11, 15, 19, 31, 47 (mod 52), a(p) divides p + 1, but a(p) does not divide (p + 1)/2. a(n) <= (12/7)*n for all n, where the equality holds if and only if n = 2*7^e, e >= 1. LINKS Jianing Song, Table of n, a(n) for n = 1..5000 FORMULA a(m*n) = a(m)*a(n) if gcd(m, n) = 1. For odd primes p, a(p^e) = p^(e-1)*a(p) if p^2 does not divide a(p). Any counterexample would be a 3-Wall-Sun-Sun prime. a(2^e) = 3 if e = 1, 6 if e = 2 and 3*2^(e-2) if e >= 3. a(13^e) = 13^e, e >= 1. PROG (PARI) A006190(m) = ([3, 1; 1, 0]^m)[2, 1] a(n) = my(i=1); while(A006190(i)%n!=0, i++); i CROSSREFS Let {x(n)} be a sequence defined by x(0) = 0, x(1) = 1, x(n+2) = k*x(n+1) + x(n). Then the periods, ranks and the ratios of the periods to the ranks modulo a given integer n are given by: k = 1: A001175 (periods), A001177 (ranks), A001176 (ratios). k = 2: A175181 (periods), A214028 (ranks), A214027 (ratios). k = 3: A175182 (periods), this sequence (ranks), A322906 (ratios). Sequence in context: A011209 A182649 A257698 * A071018 A144559 A155114 Adjacent sequences:  A322904 A322905 A322906 * A322908 A322909 A322910 KEYWORD nonn AUTHOR Jianing Song, Jan 05 2019 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 October 19 21:18 EDT 2021. Contains 348091 sequences. (Running on oeis4.)