_Robert G. Wilson v (rgwv(AT)rgwv.com), _, Jan 15 2001

(BASIC?): 10 ! Improperly Reduced Fibonacci SeqSequence. 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

nonn,new

nonn

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

0,4

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.

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} ]

(BASIC?): 10 ! Improperly Reduced Fibonacci Seq. 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

Cf. A000045.

nonn

Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 15 2001

approved