A055171 Cumulative counting sequence: method B (noun,adjective)-pairs with first term 1.

1, 1, 1, 1, 3, 1, 4, 3, 1, 1, 6, 3, 2, 4, 1, 1, 8, 3, 3, 4, 2, 6, 1, 2, 1, 1, 11, 3, 5, 4, 3, 6, 2, 2, 3, 8, 1, 1, 13, 3, 8, 4, 4, 6, 3, 2, 5, 8, 2, 11, 1, 5, 1, 1, 16, 3, 10, 4, 6, 6, 4, 2, 7, 8, 4, 11, 2, 5, 3, 13, 1, 1, 18, 3, 12, 4, 9, 6, 6, 2, 9, 8, 5, 11, 3, 5

Offset: 1

Author

Clark Kimberling, Apr 27 2000

Keywords

• nonn

Comments

Segments (generated as at A055168): 1; 1,1; 1,3; 1,4,3,1; 1,6,3,2,4,1; ...

Conjecture: every positive integer occurs.

Examples

			Write 1, thus having 1 once, thus having 1 3 times, thus having 1 4 times and 3 once, etc.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055168.

Programs

Mathematica

s = {1}; Do[s = Flatten[{s, {#,Count[s, #]} & /@ DeleteDuplicates[s]}], {24}]; s (* Peter J. C. Moses, Mar 21 2013 *)

Python

from collections import Counter
from sympy import flatten
t = [1]
[t.extend(flatten(Counter(t).items())) for _ in range(10)]
print(t) # Nicholas Stefan Georgescu, Jan 16 2025