OFFSET
1,4
COMMENTS
Write 0 followed by segments defined inductively as follows: each segment
tells how many times each previously written integer occurs, in the order
of first occurrence. This is Method A (adjective-before-noun pairs); for
definition and differs from A217760 beginning at the 62nd term.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..9666
Clark Kimberling, Unsolved Problems and Rewards, Problem 4
EXAMPLE
Start with 0, followed by the adjective-noun pair 1,0; followed by
adjective-noun pairs 2,0 then 1,1; etc. Writing the pairs vertically,
the initial segments are
0..1..2 1..3 3 1..4 5 2 2..5 6 5 3 1 1..6 9 6 5 2 4 1..7 11 8 6 4 6 4 1
...0..0 1..0 1 2..0 1 2 3..0 1 2 3 4 5..0 1 2 3 4 5 6..0 1 2 3 4 5 6 9
The order of appearance is 0,1,2,3,4,5,6,9,7,11,8,... conjectured at A055170 to include all the nonnegative integers.
MATHEMATICA
s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* A217760 *)
s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ (a = DeleteDuplicates[s])}], {24}]; a; (* A055170 *) (* Peter J. C. Moses, Mar 21 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 24 2013
STATUS
approved