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%I #29 Oct 21 2022 22:00:17
%S 9,81,65,61,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,
%T 145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,
%U 89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145
%N Take sum of squares of digits of previous term; start with 9.
%D R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.
%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) = A000218(n+1). - _R. J. Mathar_, May 24 2008
%F a(n) = A080709(n-2) for n > 4. - _M. F. Hasler_, May 24 2009
%t Nest[Append[#, Total[IntegerDigits[Last@ #]^2]] &, {9}, 79] (* _Michael De Vlieger_, Apr 29 2018 *)
%t NestList[Total[IntegerDigits[#]^2]&,9,80] (* or *) PadRight[ {9,81,65,61},80,{42,20,4,16,37,58,89,145}] (* _Harvey P. Dale_, Sep 11 2019 *)
%o From _M. F. Hasler_, May 24 2009: (Start)
%o (PARI) A008463(n)=[9,81,65,61,37, 58,89,145,42,20,4,16][if(n>12,(n-5)%8+5,n)]
%o /* This code has been checked as follows: */
%o k=3;vector(99,n,k=A003132(k))==vector(99,n,A008463(n))
%o /* The given terms have been checked as follows: */
%o a=[/* paste the terms here */]; apply(A008463,[1..#a])==a \\ (End)
%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), 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_
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