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Search: id:A099645
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| A099645 |
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Number of iterations until n reaches a number in A039943 under "x goes to sum of squares of digits of x" map. |
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+0
14
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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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.
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REFERENCES
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A. Porges, A set of eight numbers, Amer. Math. Monthly, 52 (1945), 379-382. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
Hugo Steinhaus: "Sto zadan" (1958), "One Hundred Problems in Elementary Mathematics" (1964), problem 2. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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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.
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MATHEMATICA
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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}];
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PROGRAM
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(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} [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
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CROSSREFS
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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). [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
Sequence in context: A092173 A062521 A157700 this_sequence A167260 A137520 A010676
Adjacent sequences: A099642 A099643 A099644 this_sequence A099646 A099647 A099648
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KEYWORD
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base,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 08 2004
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EXTENSIONS
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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. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
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