A092400 Fixed point of the morphism 1 -> 1121211, 2 -> 1121212121211, starting from a(1) = 1.

1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1

Offset

1,3

Comments

Length of n-th run of identical symbols in A051069.

Links

Table of n, a(n) for n=1..105.

Index entries for sequences that are fixed points of mappings

Formula

Sum_{k=1..n} a(k) = A007417(n).

Mathematica

Nest[ Function[ l, {Flatten[(l /. {1 -> {1, 1, 2, 1, 2, 1, 1}, 2 -> {1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1}})]}], {1}, 3] (* Robert G. Wilson v, Feb 26 2005 *)

Prog

(Python)
from sympy import integer_log
def A007417(n):
    def f(x): return n+x-sum(((m:=x//9**i)-2)//3+(m-1)//3+2 for i in range(integer_log(x, 9)[0]+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m
def A092400(n): return A007417(n)-A007417(n-1) if n>1 else 1 # Chai Wah Wu, Feb 16 2025

Crossrefs

Cf. A007417, A051069.

Sequence in context: A184240 A244840 A103414 * A303598 A337277 A269974

Adjacent sequences: A092397 A092398 A092399 * A092401 A092402 A092403

Keyword

easy,nonn

Author

Philippe Deléham, Mar 21 2004

Extensions

More terms from Robert G. Wilson v, Feb 26 2005

Status

approved