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%I #41 Feb 16 2024 10:21:33
%S 4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,
%T 20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,
%U 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 4.
%C Occurs as puzzle in the Nintendo DS game "Professor Layton and the Diabolical Box". - _M. F. Hasler_, Dec 18 2009
%C From _M. F. Hasler_, Apr 27 2018: (Start)
%C 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 Porges gave his "set of eight numbers" as a(1)..a(8) in this order, rather than that of the set A039943. (End)
%D R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.
%H Vincenzo Librandi, <a href="/A080709/b080709.txt">Table of n, a(n) for n = 1..100</a>
%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 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.
%F a(n) = A000216(n+1). - _R. J. Mathar_, Sep 19 2008
%F 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 NestList[Total[IntegerDigits[#]^2]&, 4, 80] (* _Vincenzo Librandi_, Jan 29 2013 *)
%o (PARI) A080709(n)=[4, 16, 37, 58, 89, 145, 42, 20][(n-1)%8+1] \\ _M. F. Hasler_, May 24 2009
%o (Haskell)
%o a080709 n = a080709_list !! (n-1)
%o a080709_list = iterate a003132 4
%o -- _Reinhard Zumkeller_, Aug 24 2011
%o (Magma) &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, 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 nonn,base,easy
%O 1,1
%A _N. J. A. Sloane_, Mar 04 2003
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