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

Author

Vladimir Shevelev, Apr 25 2010

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000045, A176744, A176745.

Programs

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

Extensions

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