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

1,2

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.

Links

Table of n, a(n) for n=1..44.

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

Example

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.

Crossrefs

Cf. A002487, A013583.

Sequence in context: A245205 A101643 A334136 * A203848 A160404 A103736

Adjacent sequences: A046812 A046813 A046814 * A046816 A046817 A046818

Keyword

nonn

Author

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

Status

approved