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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).
1
2, 3, 5, 15, 13, 38, 93, 106, 89, 695, 233, 1492, 1821, 3932, 1597, 12895, 16708, 13526, 76573, 70828, 28657, 787967, 1125255, 4005507, 6087997, 10487301, 514229, 30784111, 68658699, 150301527, 38770237, 290846217, 525964251, 164233751, 193262488, 1368085495, 1075181473, 8903068701, 10762707995, 4554542743, 433494437
OFFSET
1,1
COMMENTS
The subsequence of prime terms is A005478; a term is prime if and only if it is a Fibonacci prime (proved by Giovanni Resta).
LINKS
FORMULA
a(n+1) = A056240(A001414(a(n)) + A001414(a(n-1))).
a(n) = A056240(A000045(n+2)). - Giovanni Resta, Jan 07 2020
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved