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%I #60 Dec 14 2023 06:01:56
%S 2,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,
%T 42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,
%U 145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37
%N Take sum of squares of digits of previous term, starting with 2.
%C As the orbit of 2 under A003132, this could also have offset 0. Merges into A080709 right after the first term: a(n+1) = A080709(n) for all n >= 1. - _M. F. Hasler_, Apr 27 2018
%D R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.
%D P. Kiss, A generalization of a problem in number theory, Math. Sem. Notes Kobe Univ., 5 (1977), no. 3, 313-317. MR 0472667 (57 #12362).
%H Vincenzo Librandi, <a href="/A000216/b000216.txt">Table of n, a(n) for n = 1..100</a>
%H H. G. Grundmann, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Grundman/grundman7.html">Semihappy Numbers</a>, J. Int. Seq. 13 (2010), 10.4.8, Theorem 1.
%H P. Kiss, <a href="http://real-j.mtak.hu/9373/1/MTA_MatematikaiLapok_1974.pdf">A generalization of a problem in number theory</a>, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149.
%H Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382.
%H A. Porges, <a href="/A003621/a003621.pdf">A set of eight numbers</a>, Amer. Math. Monthly, 52 (1945), 379-382. [Annotated scanned copy]
%H H. J. J. te Riele, <a href="https://ir.cwi.nl/pub/6662">Iteration of number-theoretic functions</a>, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1).
%F Periodic with period 8.
%t NestList[Total[IntegerDigits[#]^2]&, 2, 80] (* _Vincenzo Librandi_, Jan 29 2013 *)
%o (PARI) A000216(n)=[42, 20, 4, 16, 37, 58, 89, 145, 2][n%8+8^(n<2)] \\ _M. F. Hasler_, May 24 2009, edited Apr 27 2018
%o (Haskell) a000216 n = a000216_list !! (n-1)
%o a000216_list = iterate a003132 2 -- _Reinhard Zumkeller_, Aug 24 2011
%o (Magma) [2] cat &cat[[4, 16, 37, 58, 89, 145, 42, 20]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013
%Y Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000218 (starting with 3), A080709 (starting with 4), A000221 (starting with 5), A008460 (starting with 6), A008462 (starting with 8), A008463 (starting with 9), A139566 (starting with 15), A122065 (starting with 74169). - _M. F. Hasler_, May 24 2009
%K nonn,base,easy
%O 1,1
%A _N. J. A. Sloane_
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