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%I
%S 2,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,
%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
%N Take sum of squares of digits of previous term.
%D R. Honsberger, Ingenuity in Math., Random House, 1970, p. 83.
%D A. Porges, A set of eight numbers, Amer. Math. Monthly, 52 (1945), 379-382.
%H Vincenzo Librandi, <a href="/A000216/b000216.txt">Table of n, a(n) for n = 1..100</a>
%F Periodic with period 8.
%F a(n)=(1/224)*{1027*(n mod 8)+3295*[(n+1) mod 8]-1157*[(n+2) mod 8]-457*[(n+3) mod 8]-177*[(n+4) mod 8]-177*[(n+5) mod 8]+75*[(n+6) mod 8]+859*[(n+7) mod 8]}-18*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava_, Oct 21 2008]
%t NestList[Total[IntegerDigits[#]^2]&, 2, 80] (* _Vincenzo Librandi_, Jan 29 2013 *)
%o (PARI) A000216(n)=[2, 4, 16, 37, 58, 89, 145, 42, 20][n%8+8*(n%8<2 & n>1)] \\\\ [From _M. F. Hasler_, May 24 2009]
%o (Haskell)
%o a000216 n = a000216_list !! (n-1)
%o a000216_list = iterate a003132 2
%o -- _Reinhard Zumkeller_, Aug 24 2011
%o (MAGMA) [2] cat &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, 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). [From _M. F. Hasler_, May 24 2009]
%K nonn,base,easy
%O 1,1
%A _N. J. A. Sloane_.
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