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A064434 a(n) = (2*a(n-1) + 1) mod n. 4
0, 1, 0, 1, 3, 1, 3, 7, 6, 3, 7, 3, 7, 1, 3, 7, 15, 13, 8, 17, 14, 7, 15, 7, 15, 5, 11, 23, 18, 7, 15, 31, 30, 27, 20, 5, 11, 23, 8, 17, 35, 29, 16, 33, 22, 45, 44, 41, 34, 19, 39, 27, 2, 5, 11, 23, 47, 37, 16, 33, 6, 13, 27, 55, 46, 27, 55, 43, 18, 37, 4, 9, 19, 39, 4, 9, 19, 39, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) is the remainder when (2*a(n-1) + 1) is divided by n.

Can be generalized to a(n) = f(a(n-1)) mod n, where f is any polynomial function.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = (a(n-1) * 2 + 1) mod n.

EXAMPLE

0, (0*2+1) mod 2 = 1, (1*2+1) mod 3 = 0, (0*2+1) mod 4 = 1, (1*2+1) mod 5 = 3 (3*2+1) mod 6 = 1.

MATHEMATICA

nxt[{n_, a_}]:={n+1, Mod[2a+1, n+1]}; Transpose[NestList[nxt, {1, 0}, 80]][[2]] (* Harvey P. Dale, Feb 10 2014 *)

PROG

(PARI) { a=0; for (n=1, 1000, a=(2*a + 1)%n; write("b064434.txt", n, " ", a); ) } \\ Harry J. Smith, Sep 13 2009

(MAGMA) [n le 1 select n-1 else (2*Self(n-1)+1) mod n: n in [1..80]]; // Vincenzo Librandi, Jun 24 2018

(GAP) a:=[0];; for n in [2..90] do a[n]:=(2*a[n-1]+1) mod n; od; a; # Muniru A Asiru, Jun 24 2018

CROSSREFS

Cf. A064456, A079878.

Sequence in context: A280995 A092689 A281553 * A328988 A086401 A095732

Adjacent sequences:  A064431 A064432 A064433 * A064435 A064436 A064437

KEYWORD

nonn

AUTHOR

Jonathan Ayres (JonathanAyres(AT)btinternet.com), Oct 01 2001

STATUS

approved

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Last modified July 28 07:46 EDT 2021. Contains 346321 sequences. (Running on oeis4.)