OFFSET
1,1
COMMENTS
a(n) is the least k such that A358005(k) = n.
Conjecture: there are no other terms.
EXAMPLE
a(1) = 19 because 19 = 1 + 2 + 3 + 5 + 8 and no smaller number is the sum of 5 distinct positive Fibonacci numbers in exactly 1 way.
a(2) = 45 because 45 = 1 + 2 + 3 + 5 + 34
= 1 + 2 + 8 + 13 + 21 and no smaller number is the sum of 5 distinct positive Fibonacci numbers in exactly 2 ways.
a(3) = 71 because 71 = 1 + 2 + 5 + 8 + 55
= 1 + 2 + 13 + 21 + 34
= 3 + 5 + 8 + 21 + 34 and no smaller number is the sum of 5 distinct positive Fibonacci numbers in exactly 3 ways.
a(4) = 160 because 160 = 1 + 2 + 5 + 8 + 144
= 1 + 2 + 13 + 55 + 89
= 3 + 5 + 8 + 55 + 89
= 3 + 13 + 21 + 34 + 89 and no smaller number is the sum of 5 distinct positive Fibonacci numbers in exactly 4 ways.
a(5) = 414 because 414 = 1 + 2 + 13 + 21 + 377
= 1 + 2 + 34 + 144 + 233
= 3 + 5 + 8 + 21 + 377
= 3 + 13 + 21 + 144 + 233
= 3 + 34 + 55 + 89 + 233 and no smaller number is the sum of 5 distinct positive Fibonacci numbers in exactly 5 ways.
a(6) = 1084 because 1084 = 1 + 2 + 5 + 89 + 987
= 3 + 5 + 34 + 55 + 987
= 3 + 5 + 89 + 377 + 610
= 8 + 13 + 21 + 55 + 987
= 8 + 34 + 55 + 377 + 610
= 8 + 89 + 144 + 233 + 610 and no smaller number is the sum of 5 distinct positive Fibonacci numbers in exactly 6 ways.
MAPLE
G:= mul(1+t*x^combinat:-fibonacci(k), k=2..17):
S:= coeff(expand(G), t, 5):
V:= Vector(6):
for i from 19 to combinat:-fibonacci(18) do
v:= coeff(S, x, i);
if v > 0 and V[v] = 0 then V[v]:= i fi
od:
convert(V, list);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Jan 06 2023
STATUS
approved