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A082090 Length of iteration sequence if function A056239, a pseudo-logarithm is iterated and started at n. Fixed point equals zero for all initial values. 3
2, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 7, 6, 6, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Mohammad K. Azarian, On the Fixed Points of a Function and the Fixed Points of its Composite Functions, International Journal of Pure and Applied Mathematics, Vol. 46, No. 1, 2008, pp. 37-44.  Mathematical Reviews, MR2433713 (2009c:65129), March 2009.  Zentralblatt MATH, Zbl 1160.65015.

Mohammad K. Azarian, Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal, Vol. 38, No. 1, January 2007, p. 60.  Solution published in Vol. 39, No. 1, January 2008, pp. 66-67.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

EXAMPLE

n=127:list={127,31,11,5,3,2,1,0},a[127]=8

MAPLE

f:= n-> add (numtheory[pi](i[1])*i[2], i=ifactors(n)[2]):

a:= n-> 1+ `if`(n=1, 1, a(f(n))):

seq (a(n), n=1..120);  # Alois P. Heinz, Aug 09 2012

MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] bpi[x_] := Table[PrimePi[Part[ba[x], j]], {j, 1, lf[x]}] api[x_] := Apply[Plus, ep[x]*bpi[x]] Table[Length[FixedPointList[api, w]]-1, {w, 2, 128}]

CROSSREFS

Cf. A056239, A008475, A001414, A082083-A082086, A082091.

Sequence in context: A088527 A030602 A133947 * A060197 A116487 A249041

Adjacent sequences:  A082087 A082088 A082089 * A082091 A082092 A082093

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 09 2003

STATUS

approved

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Last modified November 19 19:18 EST 2019. Contains 329323 sequences. (Running on oeis4.)