A058981 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..100.

EXAMPLE

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.

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} ]

PROG

(BASIC?): 10 ! Improperly Reduced Fibonacci Sequence. 20 Option Base 1 @ Dim F(1), S$[65530] 30 Z=1 @ Y=0 @ F(1)=1 40 S$='0, 1, ' @ C=1 @ D=1 100 C=C+1 110 N=Y+Z 120 For I=1 To D 140 If Not Rmd(N, F(I)) Then 160 150 Next I @ D=D+1 @ Dim F(D) @ Goto 180 160 N=N/F(I) 170 For I=I To D-1 @ F(I)=F(I+1) @ Next I 180 F(D)=N @ S$=S$&Str$(N)&', ' 190 Y=Z @ Z=N 200 Goto 100

CROSSREFS

Cf. A000045.

Sequence in context: A137403 A082233 A330806 * A117339 A096016 A123274

Adjacent sequences: A058978 A058979 A058980 * A058982 A058983 A058984

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jan 15 2001

STATUS

approved