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 A080709 #41 Feb 16 2024 10:21:33 %S A080709 4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42, %T A080709 20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145, %U A080709 42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37 %N A080709 Take sum of squares of digits of previous term, starting with 4. %C A080709 Occurs as puzzle in the Nintendo DS game "Professor Layton and the Diabolical Box". - _M. F. Hasler_, Dec 18 2009 %C A080709 From _M. F. Hasler_, Apr 27 2018: (Start) %C A080709 As the orbit of 4 under A003132, this could rather have offset 0. Merges with the orbit of 5 at the 5th term of both sequences, and with other orbits as given in the formula section. %C A080709 Porges gave his "set of eight numbers" as a(1)..a(8) in this order, rather than that of the set A039943. (End) %D A080709 R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83. %H A080709 Vincenzo Librandi, <a href="/A080709/b080709.txt">Table of n, a(n) for n = 1..100</a> %H A080709 Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382. %H A080709 <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 A080709 Periodic with period 8. %F A080709 a(n) = A000216(n+1). - _R. J. Mathar_, Sep 19 2008 %F A080709 By definition, a(n+1) = A003132(a(n)) for n >= 1. a(n) = A000221(n) = A000218(n+3) = A008460(n+6) = A008462(n+1) = A008463(n+2) = A122065(n+3) = A139566(n+2) for n >= 8 or earlier. - _M. F. Hasler_, May 24 2009, edited Apr 27 2018 %t A080709 NestList[Total[IntegerDigits[#]^2]&, 4, 80] (* _Vincenzo Librandi_, Jan 29 2013 *) %o A080709 (PARI) A080709(n)=[4, 16, 37, 58, 89, 145, 42, 20][(n-1)%8+1] \\ _M. F. Hasler_, May 24 2009 %o A080709 (Haskell) %o A080709 a080709 n = a080709_list !! (n-1) %o A080709 a080709_list = iterate a003132 4 %o A080709 -- _Reinhard Zumkeller_, Aug 24 2011 %o A080709 (Magma) &cat[[4, 16, 37, 58, 89, 145, 42, 20]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013 %Y A080709 Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), 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 A080709 nonn,base,easy %O A080709 1,1 %A A080709 _N. J. A. Sloane_, Mar 04 2003