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 A254123 Least number of terms needed to build n from Fibonacci numbers using + and *. 2
 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 1, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = 1 iff n is a Fibonacci number (A000045). a(n) = 2 iff n is in A254122. a(A025282(n)) = n. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(40) = 2 because 40 = 5*8; 5 and 8 are Fibonacci numbers but 40 is not. MAPLE N:= 1000: # to get a(1) to a(N) A:= Vector(N): for i from 1 do f:= combinat:-fibonacci(i); if f > N then break fi; A[f]:= 1 od: for n from 1 to N do if A[n] = 0 then m:= floor(n/2); r:= min(A[1..m] + A[[seq(n-i, i=1..m)]]); for a in select(`<=`, numtheory:-divisors(n) minus {1}, floor(sqrt(n))) do r:= min(r, A[a] + A[n/a]) od: A[n]:= r; fi od: seq(A[i], i=1..N); CROSSREFS Cf. A000045, A025282, A254122. Sequence in context: A352884 A102382 A024890 * A007895 A053260 A267135 Adjacent sequences: A254120 A254121 A254122 * A254124 A254125 A254126 KEYWORD nonn AUTHOR Robert Israel, Jan 25 2015 STATUS approved

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Last modified July 19 12:04 EDT 2024. Contains 374394 sequences. (Running on oeis4.)