A046815 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.

1, 3, 8, 21, 24, 144, 58, 63, 147, 155, 152, 173, 168, 385, 398, 461, 406, 401, 435, 1215, 440, 1016, 1011, 1063, 1053, 1045, 1066, 2608, 1050, 1139, 1160, 2650, 2642, 1155, 2663, 2807, 2647, 6841, 2969, 2749, 2736, 7145, 2757, 2791

Offset: 1

Author

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

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Marjorie Bicknell-Johnson, The least integer having p Fibonacci representations (p prime), Fibonacci Quarterly 40 (2002), pp. 260-265.

Crossrefs

Cf. A002487, A013583.