A272136 a(n+1) = a(n-1) + A001414(a(n)) with a(1)=1, a(2)=2.

1, 2, 3, 5, 8, 11, 19, 30, 29, 59, 88, 76, 111, 116, 144, 130, 164, 175, 181, 356, 274, 495, 296, 538, 567, 557, 1124, 842, 1547, 879, 1843, 995, 2047, 1107, 2097, 1346, 2772, 1374, 3006, 1549, 4555, 2465, 4606, 2528, 4695, 2849, 4750, 2885, 5332, 2963, 8295

Offset

1,2

Comments

Replace the Fibonacci rule a(n) = a(n-2) + a(n-1) by a(n) = a(n-2) + (sum of prime factors with repetition of a(n-1)).

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

a(3)=a(1)+A001414(2) = 1+2 = 3. a(4)=2+3=5, a(5)=3+5=8, a(6)=5+6=11; etc.

Mathematica

a[n_]:= a[n] = If[n < 3, n, a[n-2] + Plus @@ Times @@@ FactorInteger@ a[n-1]]; Array[a, 50] (* Giovanni Resta, Apr 24 2016 *)

Crossrefs

Cf. A000045, A001414.

Sequence in context: A065462 A062762 A004693 * A254308 A119014 A006258

Adjacent sequences: A272133 A272134 A272135 * A272137 A272138 A272139

Keyword

nonn

Author

David James Sycamore, Apr 21 2016

Extensions

a(41)-a(51) from Giovanni Resta, Apr 24 2016

Status

approved