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 A000221 #49 Jul 04 2025 08:32:22
%S A000221 5,25,29,85,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,
%T A000221 20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,
%U A000221 42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145
%N A000221 Take sum of squares of digits of previous term; start with 5.
%C A000221 Essentially the same as A080709, cf. formula. - _M. F. Hasler_, May 24 2009
%C A000221 As the orbit of 5 under A003132, this could as well start with index 0. - _M. F. Hasler_, Apr 27 2018
%D A000221 R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.
%D A000221 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 25.
%H A000221 Vincenzo Librandi, <a href="/A000221/b000221.txt">Table of n, a(n) for n = 1..100</a>
%H A000221 Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382.
%H A000221 <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 A000221 Ultimately periodic with period 8.
%F A000221 a(n) = A080709(n) for n >= 5. - _M. F. Hasler_, May 24 2009
%F A000221 a(n+1) = A003132(a(n)). - _Reinhard Zumkeller_, Dec 19 2011
%t A000221 NestList[Plus @@ IntegerDigits[ # ]^2 &, 5, 50]
%t A000221 PadRight[{5,25,29,85},120,{4,16,37,58,89,145,42,20}] (* _Harvey P. Dale_, Jan 14 2022 *)
%o A000221 (PARI) A000221(n)=[20,4,16,37,58,89,145,42,5,25,29,85][n%8+8^(n<5)] \\ _M. F. Hasler_, May 24 2009, edited Apr 27 2018
%o A000221 (Magma) [5, 25, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013
%o A000221 (Haskell)
%o A000221 a000221 n = a000221_list !! (n-1)
%o A000221 a000221_list = iterate a003132 5
%o A000221 -- _Reinhard Zumkeller_, Mar 04 2013
%Y A000221 Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), 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 A000221 nonn,base,easy,nice
%O A000221 1,1
%A A000221 _N. J. A. Sloane_