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A008463 Take sum of squares of digits of previous term; start with 9.

%I A008463 #29 Oct 21 2022 22:00:17
%S A008463 9,81,65,61,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,
%T A008463 145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,
%U A008463 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 A008463 Take sum of squares of digits of previous term; start with 9.
%D A008463 R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.
%H A008463 Arthur Porges, <a href="http://www.jstor.org/stable/2304639">A set of eight numbers</a>, Amer. Math. Monthly 52 (1945), 379-382.
%H A008463 <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 A008463 Periodic with period 8.
%F A008463 a(n) = A000218(n+1). - _R. J. Mathar_, May 24 2008
%F A008463 a(n) = A080709(n-2) for n > 4. - _M. F. Hasler_, May 24 2009
%t A008463 Nest[Append[#, Total[IntegerDigits[Last@ #]^2]] &, {9}, 79] (* _Michael De Vlieger_, Apr 29 2018 *)
%t A008463 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 A008463 From _M. F. Hasler_, May 24 2009: (Start)
%o A008463 (PARI) A008463(n)=[9,81,65,61,37, 58,89,145,42,20,4,16][if(n>12,(n-5)%8+5,n)]
%o A008463 /* This code has been checked as follows: */
%o A008463 k=3;vector(99,n,k=A003132(k))==vector(99,n,A008463(n))
%o A008463 /* The given terms have been checked as follows: */
%o A008463 a=[/* paste the terms here */]; apply(A008463,[1..#a])==a \\ (End)
%Y A008463 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 A008463 nonn,base,easy
%O A008463 1,1
%A A008463 _N. J. A. Sloane_