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

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, 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, 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

Offset: 1

Author

Colm Mulcahy, Mar 04 2008

Keywords

• easy
• nonn

Examples

			a(5) = 3 because the Zeckendorf representation of the 5th prime is 11 = 3 + 8.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A138182, A138183.

Programs

Python

from sympy import prime
def A138182(n):
    m, tlist = prime(n), [1,2]
    while tlist[-1]+tlist[-2] <= m:
        tlist.append(tlist[-1]+tlist[-2])
    for d in tlist[::-1]:
        if d == m:
            return d
        elif d < m:
            m -= d # Chai Wah Wu, Jun 14 2018

Formula

a(n) = A139764(A000040(n)). [From R. J. Mathar, Oct 23 2010]

Extensions

a(8) replaced by 1. Sequence extended beyond a(18) - R. J. Mathar, Oct 23 2010