A214635 Period of A213437 mod n.

1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 4, 1, 3, 1, 6, 3, 1, 3, 1, 1, 1, 1, 3, 4, 3, 1, 1, 3, 1, 1, 1, 6, 3, 3, 1, 1, 4, 3, 7, 1, 1, 1, 3, 1, 4, 1, 6, 3, 6, 4, 1, 3, 3, 1, 1, 1, 3, 3, 10, 1, 3, 1, 12, 1, 1, 6, 1, 3, 11, 3, 6, 1, 3, 1, 1, 4, 4, 3, 9, 7, 5, 1, 6, 1, 1, 1, 14, 3, 4, 1, 1, 4, 3, 1, 3, 6, 3

Offset

1,5

Links

Table of n, a(n) for n=1..99.

Formula

Empirically:

A214635(2^n) = 1, A214635(5^n) = A214635(10^n) = 3, for all n>0.

A214635(3^n) = A214635(6^n) = (1, 3, 3, 9, 27, 81, ...) = 3^(n-2) for n>2.

A214635(15^n) = (3,3,3,9,27,81,...) = A214635(3^n) for n>1.

A214635(7^n) = (1,6,42,294,...) = 6*7^(n-2) for n>1.

A214635(11^n) = (1,20,220,2420,...) = 20*11^(n-2) for n>1. - M. F. Hasler, Jul 24 2012

Prog

(PARI) A214635(n, N=99)={my(a=[Mod(1, n)]); for(n=1, N-1, a=concat(a, a[n]+(a[n]+1)*prod(k=1, n-1, a[k]))); for(p=1, N\3, forstep(m=N, p+1, -1, a[m]==a[m-p]&next; 3*m>N&next(2); return(p)); return(p))} /* the 2nd optional parameter must be taken large enough, at least 3 times the period length and starting position. The script returns zero if the period is not found (probably due to these constraints). */

Crossrefs

Cf. A213437, A214636.

Sequence in context: A176187 A180683 A365331 * A166030 A351149 A191523

Adjacent sequences: A214632 A214633 A214634 * A214636 A214637 A214638

Keyword

nonn

Author

David Applegate, M. F. Hasler and N. J. A. Sloane, Jul 23 2012

Status

approved