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Smallest number which can be written as the sum of distinct Fibonacci numbers in n ways and such that the Zeckendorf representation of the number uses only even-subscripted Fibonacci numbers.
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%I #7 Jan 22 2019 17:29:02

%S 1,3,8,21,24,144,58,63,147,155,152,173,168,385,398,461,406,401,435,

%T 1215,440,1016,1011,1063,1053,1045,1066,2608,1050,1139,1160,2650,2642,

%U 1155,2663,2807,2647,6841,2969,2749,2736,7145,2757,2791

%N Smallest number which can be written as the sum of distinct Fibonacci numbers in n ways and such that the Zeckendorf representation of the number uses only even-subscripted Fibonacci numbers.

%C Each term is >= corresponding term of A013583, smallest number that can be written as sum of distinct Fibonacci numbers in n ways. Equality holds for n prime, n a Fibonacci number, n a Lucas number as well as some other cases.

%H Marjorie Bicknell-Johnson, <a href="http://www.fq.math.ca/Scanned/40-3/bicknell.pdf">The least integer having p Fibonacci representations (p prime)</a>, Fibonacci Quarterly 40 (2002), pp. 260-265.

%e a(9)=147 because 147=F(12)+F(4) and 147 is the smallest such integer having 9 representations: 147=144+3 or 144+2+1 or 89+55+3 or 89+55+2+1 or 89+34+21+3 or 89+34+21+2+1 or 89+34+13+8+3 or 89+34+13+8+2+1 or 89+34+13+5+3+2+1.

%Y Cf. A002487, A013583.

%K nonn

%O 1,2

%A Marjorie Bicknell-Johnson (marjohnson(AT)earthlink.net)