A079668 Start with 1; at n-th step, write down what is in the sequence so far.

1, 1, 1, 3, 1, 4, 1, 0, 2, 1, 3, 1, 0, 6, 1, 1, 2, 2, 3, 1, 4, 2, 0, 10, 1, 3, 2, 3, 3, 2, 4, 0, 5, 1, 6, 4, 0, 12, 1, 6, 2, 6, 3, 3, 4, 1, 5, 2, 6, 0, 7, 0, 8, 0, 9, 1, 10, 8, 0, 15, 1, 8, 2, 8, 3, 5, 4, 2, 5, 5, 6, 1, 7, 1, 8, 1, 9, 2, 10, 0, 11, 1, 12, 10

Offset

1,4

Comments

After 1 1 1 3 1, we see "4 1's, 0 2's and 1 3", so next terms are 4 1 0 2 3 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20377 (first 55 steps)

Example

Row n lists all terms written at the n-th step:
  1;
  1, 1;
  3, 1;
  4, 1,  0, 2, 1, 3;
  1, 0,  6, 1, 1, 2, 2, 3, 1, 4;
  2, 0, 10, 1, 3, 2, 3, 3, 2, 4, 0, 5, 1, 6;
  4, 0, 12, 1, 6, 2, 6, 3, 3, 4, 1, 5, 2, 6, 0, 7, 0, 8, 0, 9, 1, 10;
  ...

Maple

b:= proc(n) option remember; `if`(n<1, 0, b(n-1)+add(x^i, i=T(n))) end:
T:= proc(n) option remember; `if`(n=1, 1, (p->
      seq([coeff(p, x, i), i][], i=ldegree(p)..degree(p)))(b(n-1)))
    end:
seq(T(n), n=1..10);  # Alois P. Heinz, Aug 24 2025

Mathematica

s={1}; Do[s=Flatten[{s, {Count[s, #], #}&/@Range[Min[s], Max[s]]}], {20}]; s (* Peter J. C. Moses, Mar 21 2013 *)

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    a = [1]
    yield 1
    while True:
        counts = []
        for d in range(min(a), max(a)+1):
            c = a.count(d)
            counts.extend([c, d])
        a += counts
        yield from counts
print(list(islice(agen(), 84))) # Michael S. Branicky, Aug 24 2025

Crossrefs

For other versions see A051120, A055186, A079686.

Cf. A030717, A333867.

Sequence in context: A396109 A305100 A051512 * A144211 A393288 A260510

Adjacent sequences: A079665 A079666 A079667 * A079669 A079670 A079671

Keyword

nonn,base,tabf

Author

N. J. A. Sloane, Jan 26 2003

Extensions

More terms from Sean A. Irvine, Aug 24 2025

Status

approved