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A176746
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The Fibonacci sequence (A000045) and the integers that cannot be represented as a sum of two earlier terms in the sequence.
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2
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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
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OFFSET
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0,4
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LINKS
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EXAMPLE
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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.
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PROG
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(Sage)
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Sequence extended, definition and example rewritten by Eric M. Schmidt, Jan 26 2013
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STATUS
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approved
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