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Starting with a(1)=3, a(2)=4, a(n)=sum of digits of a(n-1) + sum of digits of a(n-2).
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%I #14 Jun 14 2023 17:51:31

%S 3,4,7,11,9,11,11,4,6,10,7,8,15,14,11,7,9,16,16,14,12,8,11,10,3,4,7,

%T 11,9,11,11,4,6,10,7,8,15,14,11,7,9,16,16,14,12,8,11,10,3,4,7,11,9,11,

%U 11,4,6,10,7,8,15,14,11,7,9,16,16,14,12,8,11,10,3,4

%N Starting with a(1)=3, a(2)=4, a(n)=sum of digits of a(n-1) + sum of digits of a(n-2).

%C Digital sum analog in base 10 of the Lucas numbers A000032 (starting at 3).

%C The sequence is periodic from n=1 with period 24.

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1).

%t nxt[{a_,b_}]:={b,Total[Flatten[IntegerDigits/@{a,b}]]}; NestList[nxt,{3,4},80][[;;,1]] (* or *) PadRight[{},80,{3,4,7,11,9,11,11,4,6,10,7,8,15,14,11,7,9,16,16,14,12,8,11,10}] (* _Harvey P. Dale_, Jun 14 2023 *)

%Y Cf. A000032.

%K nonn,base

%O 1,1

%A _Enrique Navarrete_, May 15 2017