A271901 Length of period of Narayana sequence A000930 modulo n-th prime.

7, 8, 31, 57, 60, 168, 288, 381, 528, 840, 930, 342, 1723, 1848, 46, 468, 3541, 1240, 33, 5113, 2664, 6240, 3444, 7920, 3169, 10303, 10713, 11557, 11991, 991, 2016, 130, 6256, 1610, 148, 22800, 24807, 26733, 4648, 172, 10680, 32760, 36673, 37443, 2156, 3960, 481, 12432, 226, 26220, 54523, 8160, 9680, 63000

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

H. T. Engstrom, On sequences defined by linear recurrence relations Trans. Am. Math. Soc. 33 (1) (1931) 210-218.

K. Kirthi, Narayana Sequences for Cryptographic Applications, arXiv preprint arXiv:1509.05745 [math.NT], 2015.

M. B. Nathanson, Linear recurrences and uniform distribution, Proc. Amer. Math. Soc. 48 (1975), 289-291.

D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.

Formula

a(n) = A271953(prime(n)). - Joerg Arndt, Apr 17 2016

Mathematica

a[n_] := Module[{p = Prime[n], a = 1, b = 1, c = 2, k = 1}, While[a != 1 || b != 1 || c != 1, {a, b, c} = {b, c, Mod[a + c, p]}; k++]; k];
Array[a, 100] (* Jean-François Alcover, Jul 22 2018, after Charles R Greathouse IV *)

Prog

(Python)
from sympy import prime
def A271901(n):
    p = prime(n)
    i, a, b, c =  1, 1, 1, 2 % p
    while a != 1 or b != 1 or c != 1:
        i += 1
        a, b, c = b, c, (a+c) % p
    return i # Chai Wah Wu, Feb 26 2017
(PARI) a(n, p=prime(n))=my(a=1, b=1, c=2, k=1); while(a!=1 || b!=1 || c!=1, [a, b, c]=[b, c, (a+c)%p]; k++); k \\ Charles R Greathouse IV, Feb 26 2017

Crossrefs

Cf. A000930, A271953.

Sequence in context: A136116 A329635 A080982 * A042875 A154745 A048064

Adjacent sequences: A271898 A271899 A271900 * A271902 A271903 A271904

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 17 2016

Extensions

a(1) corrected by Altug Alkan, Apr 17 2016

Terms a(24) and beyond from Joerg Arndt, Apr 17 2016

Status

approved