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%I #16 May 16 2016 06:51:11
%S 2,3,5,6,11,17,11,11,13,9,13,13,15,11,15,15,10,10,9,19,11,10,10,9,19,
%T 11,10,10,9,19,11,10,10,9,19,11,10,10,9,19,11,10,10,9,19,11,10,10,9,
%U 19,11,10,10,9,19,11,10,10,9,19,11,10,10,9,19,11,10,10,9,19,11,10,10,9,19,11,10
%N a(1)=2, a(2)=3. For n>2 a(n) is the sum of the prime factors (with repetition) of a(n-1) + a(n-2).
%C The same principle can be used to generate a family of sequences for integers m>2: a(1)=2, a(2)=3,...a(m)=m+1 and for all n > m, a(n) is the sum of the prime factors (with repetition) of the preceding m terms.
%C Example, m=3 : 2, 3, 4, 6, 13, 23, 12, 11, 25, 11, 47, 83, 50, 15, 41, 55, 40, 23,..
%C m=4 : 2, 3, 4, 5, 9, 10, 11, 12, 12, 11, 25, 12, 12, 12, 61, 97, 22, 15, ..
%C Starting from a(17) the sequence is periodic with period 10, 10, 9, 19, 11. - _Giovanni Resta_, May 15 2016
%F a(n) = A001414(a(n-1)+a(n-2)), n>=2 .
%p A268935 := proc(n)
%p option remember;
%p if n <=2 then
%p n+1;
%p else
%p A001414(procname(n-1)+procname(n-2)) ;
%p end if;
%p end proc: # _R. J. Mathar_, May 15 2016
%t a[1]=2; a[2]=3; a[n_] := a[n] = Plus @@ Times @@@ FactorInteger[ a[n-1] + a[n-2]]; Array[a, 80] (* _Giovanni Resta_, May 15 2016 *)
%K nonn
%O 1,1
%A _David James Sycamore_, Feb 16 2016
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