

A089242


Sequence is S(infinity), where S(1) = 1, S(m+1) = concatenation S(m), a(m)+1, S(m) and a(m) is the mth term of S(m). a(m) is also the mth term of the sequence.


1



1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1
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OFFSET

1,2


COMMENTS

S(m) has 2^m  1 elements and is palindromic for all m.
First occurrence of k: 1,2,4,16,65536,...,. A014221: a(n+1) = 2^a(n). This is an Ackermann function.  Robert G. Wilson v, May 30 2006


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..65536


FORMULA

a(m) = number of c's such that 0 = c(c(c(c(...c(m)...)))), where 2^c(n) is the highest power of 2 which divides evenly into n (i.e., a(m) = 1 + a(c(m))); also c(m) = A007814(m).
In other words, a(n) = number of iterates of A007814 until a zero is encountered.
Multiplicative with a(2^e) = 1 + a(e), a(p^e) = 1 for odd prime p.  Andrew Howroyd, Jul 27 2018


MATHEMATICA

c[n_] := (i++; Block[{k = 0, m = n}, While[ EvenQ[m], k++; m /= 2]; k]); f[n_] := (i = 0; NestWhile[c, n, # >= 1 &]; i); Array[f, 105] (* Robert G. Wilson v, May 30 2006 *)


CROSSREFS

Cf. A007814.
Sequence in context: A092782 A228098 A174532 * A185894 A214180 A184166
Adjacent sequences: A089239 A089240 A089241 * A089243 A089244 A089245


KEYWORD

nonn,easy,mult


AUTHOR

Leroy Quet, Dec 13 2003


EXTENSIONS

More terms from David Wasserman, Aug 31 2005


STATUS

approved



