A058981 Improperly Reduced Fibonacci Sequence: begin with a(0) = 0, a(1) = 1 and a(n) = [ a(n-1) + a(n-2) ] / a(k). a(k) is the first (not necessarily the greatest) term including 1 which divides a(n-1) + a(n-2) not previously used.

0, 1, 1, 2, 3, 5, 4, 3, 7, 2, 3, 5, 2, 1, 1, 1, 1, 2, 3, 1, 4, 5, 3, 4, 7, 11, 6, 17, 23, 10, 3, 13, 4, 1, 1, 2, 1, 3, 1, 2, 3, 5, 4, 3, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 5, 4, 3, 7, 1, 4, 1, 5, 1, 2, 1, 3, 1, 1, 2, 3, 1, 2, 1, 3, 4, 1, 5, 3, 4, 7, 11, 6, 17, 1, 6, 1, 7, 2, 3, 1, 1, 2, 1, 3, 2, 5, 1, 1, 1, 2, 1

Offset: 0

Author

Robert G. Wilson v, Jan 15 2001

Keywords

• nonn

Examples

			a(6) = 4 since a(4) + a(5) = 3 + 5 which equals 8 but is divisible by a(3) which equals 2. a(3) is no longer available for future consideration as a divisor.
		

Crossrefs

Cf. A000045.

Programs

Mathematica

y = 0; c = l = i = z = 1; d = {1}; Print[ 0 ]; Print[ 1 ]; Do[ x = y + z; c++; j = 1; While[ ! IntegerQ[ x/d[ [ j ] ] ] && j <= i, j++ ]; If[ j > i, d = Append[ d, x ]; i++, x = x / d[ [ j ] ]; d = Delete[ d, j ]; d = Append[ d, x ] ]; Print[ x ]; y = z; z = x, {n, 1, 100} ]