A214636 A213437 becomes periodic mod n starting at this position.

1, 1, 3, 2, 1, 3, 4, 3, 3, 1, 5, 3, 1, 4, 3, 4, 3, 3, 6, 2, 4, 5, 7, 3, 2, 1, 3, 4, 10, 3, 5, 4, 5, 3, 4, 3, 6, 6, 3, 3, 1, 4, 8, 5, 3, 7, 11, 4, 4, 2, 3, 2, 8, 3, 5, 4, 6, 10, 9, 3, 6, 5, 4, 5, 1, 5, 11, 3, 7, 4, 8, 3, 4, 6, 3, 6, 5, 3, 5, 4, 3, 1, 7, 4, 3, 8, 10, 5, 3, 3, 4

Offset

1,3

Links

Table of n, a(n) for n=1..91.

Formula

Empirically,

A214636(2^n) = (1,2,3,4,4,5,6,6,7,8,8,...) = A004523(n+2) for n>1.

A214636(3^n) = 3, A214636(7^n) = 4, A214636(11^n) = 5 for all n>0.

A214636(5^n) = A214636(10^n) = (1,2,5,8,11,...) = A016789(n-2) for n>1.

A214636(6^n) = (3,3,3,4,4,5,6,6,...) = A214636(2^n) for n>2.

A214636(15^n) = (3,3,5,8,11,...) = A214636(5^n) for n>2. - M. F. Hasler, Jul 24 2012

Prog

(PARI) A214636(n, N=199)={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(m-p+1)); return(1))} /* 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 (most probably due to these constraints). */

Crossrefs

Cf. A213437, A214635.

Sequence in context: A238556 A102288 A081248 * A318582 A318317 A129690

Adjacent sequences: A214633 A214634 A214635 * A214637 A214638 A214639

Keyword

nonn

Author

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

Status

approved