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

1,5

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.

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A055168.

Sequence in context: A065256 A016573 A191818 * A337209 A101038 A064883

Adjacent sequences: A055168 A055169 A055170 * A055172 A055173 A055174

Keyword

nonn

Author

Clark Kimberling, Apr 27 2000

Status

approved