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A138182 Smallest summand in the Zeckendorf representation of the n-th prime.

%I A138182 #10 Jun 14 2018 17:08:44
%S A138182 2,3,5,2,3,13,1,1,2,8,2,3,2,1,13,1,1,1,1,3,5,3,2,89,8,1,1,5,2,3,1,8,1,
%T A138182 3,5,2,13,1,2,8,1,3,13,2,1,55,1,3,2,1,233,1,8,5,3,1,2,1,2,1,3,5,1,2,1,
%U A138182 8,1,2,1,1,2,3,3,1,2,1,1,2,3,3,8,2,2,1,2,3,1,1,8,2,1,13,21,1,1,3,1,144,2,2
%N A138182 Smallest summand in the Zeckendorf representation of the n-th prime.
%H A138182 Chai Wah Wu, <a href="/A138182/b138182.txt">Table of n, a(n) for n = 1..10000</a>
%F A138182 a(n) = A139764(A000040(n)). [From _R. J. Mathar_, Oct 23 2010]
%e A138182 a(5) = 3 because the Zeckendorf representation of the 5th prime is 11 = 3 + 8.
%o A138182 (Python)
%o A138182 from sympy import prime
%o A138182 def A138182(n):
%o A138182     m, tlist = prime(n), [1,2]
%o A138182     while tlist[-1]+tlist[-2] <= m:
%o A138182         tlist.append(tlist[-1]+tlist[-2])
%o A138182     for d in tlist[::-1]:
%o A138182         if d == m:
%o A138182             return d
%o A138182         elif d < m:
%o A138182             m -= d # _Chai Wah Wu_, Jun 14 2018
%Y A138182 Cf. A138182, A138183.
%K A138182 easy,nonn
%O A138182 1,1
%A A138182 _Colm Mulcahy_, Mar 04 2008
%E A138182 a(8) replaced by 1. Sequence extended beyond a(18) - _R. J. Mathar_, Oct 23 2010