A268935 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).

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

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(n-1)+a(n-2)), n>=2 .

Maple

A268935 := proc(n)
    option remember;
    if n <=2 then
        n+1;
    else
        A001414(procname(n-1)+procname(n-2)) ;
    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[n-1] + a[n-2]]; Array[a, 80] (* Giovanni Resta, May 15 2016 *)

Crossrefs

Sequence in context: A280218 A294526 A068441 * A112598 A346721 A078913

Adjacent sequences: A268932 A268933 A268934 * A268936 A268937 A268938

Keyword

nonn

Author

David James Sycamore, Feb 16 2016

Status

approved