This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099645 #37 Jun 24 2025 10:02:53
%S A099645 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,
%T A099645 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,
%U A099645 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
%N A099645 Number of iterations until n reaches a number in A039943 under "x goes to sum of squares of digits of x" map.
%C A099645 Length of transient when the f[n]=Sum[digit^2 of n] function is iterated.
%C A099645 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.
%D A099645 Hugo Steinhaus: "Sto zadan" (1958), "One Hundred Problems in Elementary Mathematics" (1964), problem 2. - _M. F. Hasler_, May 24 2009
%H A099645 T. D. Noe, <a href="/A099645/b099645.txt">Table of n, a(n) for n = 1..1000</a>
%H A099645 Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382. - _M. F. Hasler_, May 24 2009
%e A099645 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.
%t A099645 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]]]; Table[a[n], {n, 1, 256}]
%o A099645 (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
%o A099645 (Haskell)
%o A099645 a099645 = length . takeWhile (`notElem` a039943_list) . iterate a003132
%o A099645 a099645_list = map a099645 [1..]
%o A099645 -- _Reinhard Zumkeller_, Aug 24 2011
%Y A099645 Cf. A007700, A031176.
%Y A099645 Cf. A000216, A003132, A003621
%Y A099645 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
%K A099645 base,nonn
%O A099645 1,3
%A A099645 _Labos Elemer_, Nov 08 2004
%E A099645 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