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A330988 a(1)=2, a(2)=3; then a(n+1) = smallest k such that S(k) = S(a(n)) + S(a(n-1)), (n>=2), where S is sopfr (A001414).

%I A330988 #19 Jan 22 2020 08:35:53
%S A330988 2,3,5,15,13,38,93,106,89,695,233,1492,1821,3932,1597,12895,16708,
%T A330988 13526,76573,70828,28657,787967,1125255,4005507,6087997,10487301,
%U A330988 514229,30784111,68658699,150301527,38770237,290846217,525964251,164233751,193262488,1368085495,1075181473,8903068701,10762707995,4554542743,433494437
%N A330988 a(1)=2, a(2)=3; then a(n+1) = smallest k such that S(k) = S(a(n)) + S(a(n-1)), (n>=2), where S is sopfr (A001414).
%C A330988 The subsequence of prime terms is A005478; a term is prime if and only if it is a Fibonacci prime (proved by Giovanni Resta).
%H A330988 Giovanni Resta, <a href="/A330988/b330988.txt">Table of n, a(n) for n = 1..51</a>
%F A330988 a(n+1) = A056240(A001414(a(n)) + A001414(a(n-1))).
%F A330988 a(n) = A056240(A000045(n+2)). - _Giovanni Resta_, Jan 07 2020
%e A330988 a(3)=5 since 5 is the smallest number whose sum of prime divisors is soprf(2) + sopfr(3) = 2 + 3 = 5. a(4)=15 since sopfr(3)+sopfr(5)=8, and 15 is the smallest number whose sum of prime divisors is 8.
%t A330988 sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; a[1] = 2; a[2] = 3; a[n_] := a[n] = Block[{t = sopfr@ a[n-1] + sopfr@ a[n-2], k=3}, While[ sopfr[k] != t, k++]; k]; Array[a, 21] (* _Giovanni Resta_, Jan 07 2020 *)
%Y A330988 Cf. A000045, A001414, A005478, A056240, A330821.
%K A330988 nonn
%O A330988 1,1
%A A330988 _David James Sycamore_, Jan 05 2020