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A099645 Number of iterations until n reaches a number in A039943 under "x goes to sum of squares of digits of x" map. 16
0, 1, 5, 0, 4, 9, 5, 5, 4, 1, 2, 5, 2, 6, 3, 0, 5, 3, 4, 0, 5, 6, 3, 1, 3, 2, 6, 3, 2, 5, 2, 3, 4, 4, 5, 8, 0, 2, 5, 1, 6, 0, 4, 4, 7, 4, 3, 6, 4, 4, 3, 3, 5, 7, 5, 2, 4, 0, 2, 9, 1, 2, 8, 4, 2, 7, 2, 2, 5, 5, 5, 6, 1, 3, 4, 2, 2, 4, 3, 5, 3, 3, 2, 6, 1, 2, 4, 7, 0, 4, 4, 2, 5, 4, 2, 5, 3, 1, 8, 1, 2, 5, 2, 6, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Length of transient when the f[n]=Sum[digit^2 of n] function is iterated.
In A031176 including cycle lengths[=c] of this iteration only c=1 and c=8 occur. A007770 lists cases of c=1, the happy numbers.
REFERENCES
Hugo Steinhaus: "Sto zadan" (1958), "One Hundred Problems in Elementary Mathematics" (1964), problem 2. [From M. F. Hasler, May 24 2009]
LINKS
Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382. [M. F. Hasler, May 24 2009]
EXAMPLE
n=99999999999: iteration-list={99999999999,891,146,53,34,25,29,85,89,145,42,20,[4,16,37,58,89,145,42,20],4,...]}. Lengths of transient=12, of cycle=8.
MATHEMATICA
fu[x_] :=Apply[Plus, IntegerDigits[x]^2]; hs=20; transient lengths are obtained by: a[n_] :=-1+Min[Flatten[Position[NestList[fu, n, Length[Union[NestList[fu, n, hs]]]] -Last[NestList[fu, n, Length[Union[NestList[fu, n, hs]]]]], 0]]], {n, 1, 256}];
PROG
(PARI) A099645(n)={ local( c=0, S=Set([1, 4, 16, 37, 58, 89, 145, 42, 20])); while( !setsearch(S, n), n=A003132(n); c++); c} \\ M. F. Hasler, May 24 2009
(Haskell)
a099645 = length . takeWhile (`notElem` a039943_list) . iterate a003132
a099645_list = map a099645 [1..]
-- Reinhard Zumkeller, Aug 24 2011
CROSSREFS
Cf. A039943, A031176, A007770, A000216 (orbit of 2), A000218 (orbit of 3), A080709 (orbit of 4), A000221 (orbit of 5), A008460 (orbit of 6), A008462 (orbit of 8), A008463 (orbit of 9), A139566 (orbit of 15), A122065 (orbit of 74169). - M. F. Hasler, May 24 2009
Sequence in context: A062521 A271951 A157700 * A220412 A199092 A167260
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Nov 08 2004
EXTENSIONS
Terms checked using the given PARI code. However, according to the domain of A003132 and the definition of A039943 (which both include 0), an initial a(0)=0 should be added here, too. - M. F. Hasler, May 24 2009
STATUS
approved

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Last modified June 17 15:32 EDT 2024. Contains 373456 sequences. (Running on oeis4.)