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 A000216 #60 Dec 14 2023 06:01:56 %S A000216 2,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145, %T A000216 42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89, %U A000216 145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37 %N A000216 Take sum of squares of digits of previous term, starting with 2. %C A000216 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 A000216 R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83. %D A000216 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 A000216 Vincenzo Librandi, <a href="/A000216/b000216.txt">Table of n, a(n) for n = 1..100</a> %H A000216 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 A000216 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 A000216 Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382. %H A000216 A. Porges, <a href="/A003621/a003621.pdf">A set of eight numbers</a>, Amer. Math. Monthly, 52 (1945), 379-382. [Annotated scanned copy] %H A000216 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 A000216 <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 A000216 Periodic with period 8. %t A000216 NestList[Total[IntegerDigits[#]^2]&, 2, 80] (* _Vincenzo Librandi_, Jan 29 2013 *) %o A000216 (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 A000216 (Haskell) a000216 n = a000216_list !! (n-1) %o A000216 a000216_list = iterate a003132 2 -- _Reinhard Zumkeller_, Aug 24 2011 %o A000216 (Magma) [2] cat &cat[[4, 16, 37, 58, 89, 145, 42, 20]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013 %Y A000216 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 A000216 nonn,base,easy %O A000216 1,1 %A A000216 _N. J. A. Sloane_