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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 m-th term of S(m). a(m) is also the m-th 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 21 20:18 EDT 2019. Contains 321382 sequences. (Running on oeis4.)