cp's OEIS Frontend

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

%I A176746 #10 Mar 06 2020 12:02:08
%S A176746 0,1,1,2,3,5,8,12,13,19,21,28,34,43,50,54,55,61,65,72,79,89,96,103,
%T A176746 112,118,128,135,142,144,159,174,181,188,204,210,219,226,233,237,251,
%U A176746 257,266,290,296,310,314,334,341,356,366,373,377,383,397,412,419,450
%N A176746 The Fibonacci sequence (A000045) and the integers that cannot be represented as a sum of two earlier terms in the sequence.
%e A176746 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.
%o A176746 (Sage)
%o A176746 def A176746(max) :
%o A176746     res = [0, 1]
%o A176746     fib1 = 1; fib2 = 1
%o A176746     for i in range(1, max+1) :
%o A176746         if i == fib2 :
%o A176746             res.append(i)
%o A176746             [fib1, fib2] = [fib2, fib1 + fib2]
%o A176746             continue
%o A176746         for t in res :
%o A176746             if i-t in res : break
%o A176746         else : res.append(i)
%o A176746     return res
%o A176746 # _Eric M. Schmidt_, Jan 26 2013
%Y A176746 Cf. A000045, A176744, A176745.
%K A176746 nonn
%O A176746 0,4
%A A176746 _Vladimir Shevelev_, Apr 25 2010
%E A176746 Sequence extended, definition and example rewritten by _Eric M. Schmidt_, Jan 26 2013