A182577 -id:A182577 - cp's OEIS frontend

A182578 Number of ones in Zeckendorf representation of n^n.

1, 1, 2, 3, 3, 6, 3, 10, 13, 12, 16, 15, 20, 24, 20, 30, 25, 31, 26, 33, 33, 31, 34, 42, 49, 49, 53, 55, 56, 55, 58, 64, 64, 67, 73, 78, 70, 76, 77, 75, 89, 83, 92, 90, 106, 99, 100, 99, 107, 116, 107, 115, 125, 125, 122, 119, 127, 137, 127, 138, 155, 156, 153, 160

Offset: 0

Alex Ratushnyak, May 05 2012

nonn

			5^5 = {1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0} in the Zeckendorf base.

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Cf. A007895, A020908, A020910, A025496-A025502, A182535, A182576, A182577, A000312.

def A182578(n):
    m, tlist, s = n**n, [1,2], 0
    while tlist[-1]+tlist[-2] <= m:
        tlist.append(tlist[-1]+tlist[-2])
    for d in tlist[::-1]:
        if d <= m:
            s += 1
            m -= d
    return s # Chai Wah Wu, Jun 14 2018

A276501 Smallest number k such that k! has at least n terms in its Zeckendorf representation.

Original entry on oeis.org

0, 3, 5, 5, 7, 8, 9, 9, 9, 11, 11, 14, 14, 14, 14, 14, 15, 17, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 26, 26, 26, 26, 26, 26, 26, 28, 28, 31, 31, 32, 32, 32, 34, 34, 34, 34, 34, 34, 35, 35, 35, 36, 38, 38, 38, 38, 38, 38, 38, 41, 41, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47

Offset: 1

Altug Alkan, Sep 06 2016

nonn

Least k >= 0 such that A007895(A000142(k)) >= n.

Corresponding factorial numbers are 1, 6, 120, 120, 5040, 40320, ...

			a(4) = 5 because Fibonacci(3) + Fibonacci(6) + Fibonacci(8) + Fibonacci(11) = 2 + 8 + 21 + 89 = 120 = 5!.

Chai Wah Wu, Table of n, a(n) for n = 1..10038

Cf. A000045, A000142, A007895, A182577.

a007895(n) = if(n<4, n>0, my(k=2, s, t); while(fibonacci(k++)<=n, ); while(k && n, t=fibonacci(k); if(t<=n, n-=t; s++); k--); s);
a(n) = {my(k = 0); while(a007895(k!) < n, k++); k; }

cp's OEIS Frontend

A182578 Number of ones in Zeckendorf representation of n^n.

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