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%I #38 Sep 08 2022 08:44:35
%S 8,64,52,29,85,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,
%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 145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145
%N Take sum of squares of digits of previous term; start with 8.
%D R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.
%H Vincenzo Librandi, <a href="/A008462/b008462.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) = A080709(n-1) for n >= 5 and a(n) = A000221(n-1) = A008460(n+4) for all n >= 4. - _M. F. Hasler_, May 24 2009; edited and extended Apr 27 2018
%F From _Colin Barker_, Apr 28 2018: (Start)
%F G.f.: x*(8 + 64*x + 52*x^2 + 29*x^3 + 85*x^4 + 89*x^5 + 145*x^6 + 42*x^7 + 12*x^8 - 60*x^9 - 36*x^10 + 8*x^11 - 27*x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).
%F a(n) = a(n-8) for n>13.
%F (End)
%t NestList[Total[IntegerDigits[#]^2]&, 8, 80] (* _Vincenzo Librandi_, Jan 29 2013 *)
%t PadRight[{8,64,52,29,85},80,{20,4,16,37,58,89,145,42}] (* _Harvey P. Dale_, Dec 27 2019 *)
%o (PARI) A008462(n)=[8, 64, 52, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58][if(n>13,(n-6)%8+6,n)] \\ _M. F. Hasler_, May 24 2009
%o (Magma) [8, 64, 52, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013
%o (PARI) Vec(x*(8 + 64*x + 52*x^2 + 29*x^3 + 85*x^4 + 89*x^5 + 145*x^6 + 42*x^7 + 12*x^8 - 60*x^9 - 36*x^10 + 8*x^11 - 27*x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^60)) \\ _Colin Barker_, Apr 28 2018
%Y Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), A000221 (starting with 5), A008460 (starting with 6), 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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