A176746 The Fibonacci sequence (A000045) and the integers that cannot be represented as a sum of two earlier terms in the sequence.

0, 1, 1, 2, 3, 5, 8, 12, 13, 19, 21, 28, 34, 43, 50, 54, 55, 61, 65, 72, 79, 89, 96, 103, 112, 118, 128, 135, 142, 144, 159, 174, 181, 188, 204, 210, 219, 226, 233, 237, 251, 257, 266, 290, 296, 310, 314, 334, 341, 356, 366, 373, 377, 383, 397, 412, 419, 450

Offset

0,4

Links

Table of n, a(n) for n=0..57.

Example

12 is the minimal number which is not a sum of two Fibonacci numbers. Therefore 12 is in the sequence. 13 is included because it is a Fibonacci number. 14 = 12+2 is a sum of two already included terms, so it is omitted. 19 is included as it is not a sum of two of the terms already included, namely 0,1,1,2,3,5,8,12,13.

Prog

(Sage)
def A176746(max) :
    res = [0, 1]
    fib1 = 1; fib2 = 1
    for i in range(1, max+1) :
        if i == fib2 :
            res.append(i)
            [fib1, fib2] = [fib2, fib1 + fib2]
            continue
        for t in res :
            if i-t in res : break
        else : res.append(i)
    return res
# Eric M. Schmidt, Jan 26 2013

Crossrefs

Cf. A000045, A176744, A176745.

Sequence in context: A057987 A243165 A336993 * A067288 A308075 A211181

Adjacent sequences: A176743 A176744 A176745 * A176747 A176748 A176749

Keyword

nonn

Author

Vladimir Shevelev, Apr 25 2010

Extensions

Sequence extended, definition and example rewritten by Eric M. Schmidt, Jan 26 2013

Status

approved