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%I #41 Dec 12 2023 08:35:50
%S 15,26,40,16,37,58,89,145,42,20,4,16,37,58,89,145,42,20,4,16,37,58,89,
%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
%N a(n) is the sum of squares of digits of a(n-1); a(1)=15.
%H Colin Barker, <a href="/A139566/b139566.txt">Table of n, a(n) for n = 1..1000</a>
%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.
%F a(n) = A008463(n) for n > 4. - _M. F. Hasler_, May 24 2009
%F a(n) = a(n-8) for n > 11. - _Colin Barker_, Aug 24 2015
%F G.f.: x*(36*x^10 + 6*x^9 - 27*x^8 - 145*x^7 - 89*x^6 - 58*x^5 - 37*x^4 - 16*x^3 - 40*x^2 - 26*x - 15) / ((x-1)*(x+1)*(x^2+1)*(x^4+1)). - _Colin Barker_, Aug 24 2015
%t a = {15}; Do[AppendTo[a, Plus @@ (IntegerDigits[a[[ -1]]]^2)], {70}]; a (* _Stefan Steinerberger_, Jun 14 2008 *)
%t NestList[Total[IntegerDigits[#]^2] &, 15, 70] (* or *) PadRight[ {15,26,40},70,{42,20,4,16,37,58,89,145}](* _Harvey P. Dale_, Jan 28 2013 *)
%o From _M. F. Hasler_, May 24 2009: (Start)
%o (PARI) /* to check the given terms */
%o a=[/* paste the terms here */]; a==vector(#a,n,k=if(n>1,A003132(k),15))
%o /* to check the following code, use: a==vector(99,n,A139566(n)) */
%o A139566(n)=[15,26,40,16,37,58,89,145,42,20,4][if(n>11,(n-4)%8+4,n)] \\ (End)
%o (PARI) Vec(x*(36*x^10+6*x^9-27*x^8-145*x^7-89*x^6-58*x^5-37*x^4-16*x^3 -40*x^2-26*x-15)/((x-1)*(x+1)*(x^2+1)*(x^4+1)) + O(x^70)) \\ _Colin Barker_, Aug 24 2015
%Y Cf. A101926, A087965, A074411, A110998, A051861, A048222.
%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), A122065 (starting with 74169). - _M. F. Hasler_, May 24 2009
%K base,nonn,easy
%O 1,1
%A Robert Gornall (rob(AT)khobbits.net), Jun 11 2008
%E More terms from _Stefan Steinerberger_, Jun 14 2008
%E Terms checked, using the given PARI code, by _M. F. Hasler_, May 24 2009
%E Minor edits and starting value added in name by _M. F. Hasler_, Apr 27 2018
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