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A324920 a(n) is the number of iterations of the integer splitting function (A056737) necessary to reach zero. 2
0, 1, 2, 3, 1, 2, 2, 3, 3, 1, 4, 5, 2, 3, 3, 3, 1, 2, 4, 5, 2, 2, 2, 3, 3, 1, 6, 3, 4, 5, 2, 3, 2, 4, 4, 3, 1, 2, 3, 5, 4, 5, 2, 3, 4, 2, 3, 4, 3, 1, 3, 4, 2, 3, 4, 3, 2, 2, 4, 5, 2, 3, 6, 3, 1, 4, 3, 4, 4, 3, 4, 5, 2, 3, 4, 5, 4, 2, 4, 5, 3, 1, 6, 7, 3, 3, 6, 7, 4, 5, 2, 3, 6, 5, 3, 4, 2, 3, 4, 3, 1, 2, 6, 7, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The iterations always fall to zero, proof by induction: 0 is 0; 1 -> 0; 2 -> 1; 3 -> 2; 4 -> 2; n -> some number less than n.

First occurrence of k >= 0: 0, 1, 2, 3, 10, 11, 26, 83, 178, ... see A324921.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

a(n) = 1 iff n is a perfect square (A000290).

EXAMPLE

a(0) = 0;

a(1) = 1 since 1 -> 0;

a(2) = 2 since 2 -> 1 -> 0;

a(3) = 3 since 3 -> 2 -> 1 -> 0;

a(4) = 1 since 4 -> 0; etc.

MATHEMATICA

g[n_] := Block[{d = Divisors@n}, len = Length@d; If[ OddQ@ len, 0, d[[1 + len/2]] - d[[len/2]]]]; f[n_] := Length@ NestWhileList[f, n, # > 0 &] -1; Array[f, 105, 0]

PROG

(PARI) a056737(n)=n=divisors(n); n[(2+#n)\2]-n[(1+#n)\2] \\ after M. F. Hasler in A056737

a(n) = my(x=n, i=0); while(x!=0, i++; x=a056737(x)); i \\ Felix Fröhlich, Mar 20 2019

CROSSREFS

Cf. A056737, A139693, A324921.

Sequence in context: A294233 A121884 A079087 * A236855 A244232 A227781

Adjacent sequences:  A324917 A324918 A324919 * A324921 A324922 A324923

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Mar 20 2019

STATUS

approved

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Last modified September 26 12:03 EDT 2021. Contains 347665 sequences. (Running on oeis4.)