A261082 - OEIS

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A261082

a(n) = number of steps required to reach 0 from F(n+2) by repeatedly subtracting from a natural number the number of ones in its Zeckendorf representation. Here F(n) = the n-th Fibonacci number, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, ...

1, 2, 3, 4, 6, 8, 11, 16, 24, 35, 52, 77, 114, 170, 255, 385, 584, 889, 1358, 2081, 3199, 4932, 7625, 11818, 18357, 28568, 44530, 69504, 108607, 169869, 265899, 416507, 652845, 1023946, 1607064, 2524042, 3967246, 6240680, 9825202, 15481988, 24416684, 38539840, 60880090

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..42.

FORMULA

a(n) = A219642(A000045(n+2)).

a(0) = 1; for n >= 1, a(n) = A261091(n) + a(n-1).

Other identities. For all n >= 0:

a(n) = A261081(n)+1.

PROG

(Scheme, two alternatives, the other one using memoizing definec-macro)