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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. 14
 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 T. D. Noe, Table of n, a(n) for n = 1..1000 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. A007700, A031176. Cf. A000216, A003132, A003621 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 Adjacent sequences:  A099642 A099643 A099644 * A099646 A099647 A099648 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 April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)