A000218 - OEIS

%I #47 Sep 08 2022 08:44:27

%S 3,9,81,65,61,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,

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

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

%N Take sum of squares of digits of previous term; start with 3.

%C Could also have offset 0, considered as the orbit of 3 under A003132, i.e., n-fold application of A003132 on the initial value 3. - _M. F. Hasler_, Apr 27 2018

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

%H Vincenzo Librandi, <a href="/A000218/b000218.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. Porges, <a href="/A003621/a003621.pdf">A set of eight numbers</a>, Amer. Math. Monthly, 52 (1945), 379-382. [Annotated scanned copy]

%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 Eventually periodic with period 8.

%t NestList[Total[IntegerDigits[#]^2]&, 3, 80] (* _Vincenzo Librandi_, Jan 29 2013 *)

%o (PARI) A000218(n)=[89, 145, 42, 20, 4, 16, 37, 58, 3, 9, 81, 65, 61][n%8+8^(n<6)] \\ _M. F. Hasler_, May 24 2009, edited Apr 27 2018

%o (Haskell)

%o a000218 n = a000218_list !! (n-1)

%o a000218_list = iterate a003132 3

%o -- _Reinhard Zumkeller_, Aug 24 2011

%o (Magma) [3, 9, 81, 65, 61] cat &cat[[37, 58, 89, 145, 42, 20, 4, 16]: n in [0..17]]; // _Vincenzo Librandi_, Jan 29 2013

%Y Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), 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_