

A268935


a(1)=2, a(2)=3. For n>2 a(n) is the sum of the prime factors (with repetition) of a(n1) + a(n2).


1



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, 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, 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
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OFFSET

1,1


COMMENTS

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.
Example, m=3 : 2, 3, 4, 6, 13, 23, 12, 11, 25, 11, 47, 83, 50, 15, 41, 55, 40, 23,..
m=4 : 2, 3, 4, 5, 9, 10, 11, 12, 12, 11, 25, 12, 12, 12, 61, 97, 22, 15, ..
Starting from a(17) the sequence is periodic with period 10, 10, 9, 19, 11.  Giovanni Resta, May 15 2016


LINKS

Table of n, a(n) for n=1..77.


FORMULA

a(n) = A001414(a(n1)+a(n2)), n>=2 .


MAPLE

A268935 := proc(n)
option remember;
if n <=2 then
n+1;
else
A001414(procname(n1)+procname(n2)) ;
end if;
end proc: # R. J. Mathar, May 15 2016


MATHEMATICA

a[1]=2; a[2]=3; a[n_] := a[n] = Plus @@ Times @@@ FactorInteger[ a[n1] + a[n2]]; Array[a, 80] (* Giovanni Resta, May 15 2016 *)


CROSSREFS

Sequence in context: A280218 A294526 A068441 * A112598 A078913 A174100
Adjacent sequences: A268932 A268933 A268934 * A268936 A268937 A268938


KEYWORD

nonn


AUTHOR

David James Sycamore, Feb 16 2016


STATUS

approved



