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Take sum of squares of digits of previous term; start with 5.
14

%I #46 Sep 08 2022 08:44:27

%S 5,25,29,85,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,

%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 42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,145

%N Take sum of squares of digits of previous term; start with 5.

%C Essentially the same as A080709, cf. formula. - _M. F. Hasler_, May 24 2009

%C As the orbit of 5 under A003132, this could as well start with index 0. - _M. F. Hasler_, Apr 27 2018

%D R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.

%H Vincenzo Librandi, <a href="/A000221/b000221.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 Ultimately periodic with period 8.

%F a(n) = A080709(n) for n >= 5. - _M. F. Hasler_, May 24 2009

%F a(n+1) = A003132(a(n)). - _Reinhard Zumkeller_, Dec 19 2011

%t NestList[Plus @@ IntegerDigits[ # ]^2 &, 5, 50]

%t PadRight[{5,25,29,85},120,{4,16,37,58,89,145,42,20}] (* _Harvey P. Dale_, Jan 14 2022 *)

%o (PARI) A000221(n)=[20,4,16,37,58,89,145,42,5,25,29,85][n%8+8^(n<5)] \\ _M. F. Hasler_, May 24 2009, edited Apr 27 2018

%o (Magma) [5, 25, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013

%o (Haskell)

%o a000221 n = a000221_list !! (n-1)

%o a000221_list = iterate a003132 5

%o -- _Reinhard Zumkeller_, Mar 04 2013

%Y Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), 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,nice

%O 1,1

%A _N. J. A. Sloane_