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A331466 The number of common terms in the Zeckendorf and dual Zeckendorf representations of n. 2
0, 1, 1, 0, 2, 0, 1, 2, 0, 1, 1, 1, 3, 0, 1, 1, 0, 2, 1, 2, 3, 0, 1, 1, 1, 2, 0, 1, 2, 1, 2, 2, 2, 4, 0, 1, 1, 0, 2, 1, 2, 2, 0, 1, 1, 1, 3, 1, 2, 2, 1, 3, 2, 3, 4, 0, 1, 1, 1, 2, 0, 1, 2, 1, 2, 2, 2, 3, 0, 1, 1, 0, 2, 1, 2, 3, 1, 2, 2, 2, 3, 1, 2, 3, 2, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The indices of records are numbers of the form F(2*k - 1) - 1, for k > 0, where F(k) is the k-th Fibonacci number. The corresponding record values are k - 1 = 0, 1, 2, ...

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

FORMULA

a(A000045(2*n - 1) - 1) = a(A000045(2*n) - 1) = n - 1.

a(A000045(n)) = a(A331467(n)) = 0 for n > 2.

EXAMPLE

a(6) = 1 since the Zeckendorf representation of 6 is 1001 (i.e., F(2) + F(5)), its dual Zeckendorf representation is 111 (i.e., F(2) + F(3) + F(4)), and there is only one position with a common digit 1, corresponding to the one common summand F(2).

MATHEMATICA

m = 1000; zeck = Select[Range[0, m], BitAnd[#, 2 #] == 0 &]; dualZeck = Select[Range[0, m], SequenceCount[IntegerDigits[#, 2], {0, 0}] == 0 &]; DigitCount[BitAnd[zeck[[#]], dualZeck[[#]]] & /@ Range[Min[Length[zeck], Length[dualZeck]]], 2, 1]

CROSSREFS

Cf. A000045, A007895, A014417, A104326, A112310, A331467.

Sequence in context: A294168 A299196 A227698 * A166124 A134979 A112248

Adjacent sequences:  A331463 A331464 A331465 * A331467 A331468 A331469

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Jan 17 2020

STATUS

approved

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Last modified July 31 17:34 EDT 2021. Contains 346376 sequences. (Running on oeis4.)