

A331467


Numbers with no common terms in their Zeckendorf and dual Zeckendorf representations.


2



0, 3, 5, 8, 13, 16, 21, 26, 34, 37, 42, 55, 60, 68, 71, 89, 92, 97, 110, 115, 144, 149, 157, 160, 178, 181, 186, 233, 236, 241, 254, 259, 288, 293, 301, 304, 377, 382, 390, 393, 411, 414, 419, 466, 469, 474, 487, 492, 610, 613, 618, 631, 636, 665, 670, 678, 681
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OFFSET

1,2


COMMENTS

Include all the Fibonacci numbers > 2.
The number of terms <= F(k), the kth Fibonacci number, is A000931(k + 5), for k > 3.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000


FORMULA

A331466(a(n)) = 0.


EXAMPLE

3 is a term since its Zeckendorf representation is 100 (i.e., F(4)), its dual Zeckendorf representation is 11 (i.e., F(2) + F(3)), and there is no position with the digit 1 common to both representations (i.e., the Fibonacci summands are different).


MATHEMATICA

m = 10^4; zeck = Select[Range[0, m], BitAnd[#, 2 #] == 0 &]; dualZeck = Select[Range[0, m], SequenceCount[IntegerDigits[#, 2], {0, 0}] == 0 &]; s = DigitCount[BitAnd[zeck[[#]], dualZeck[[#]]] & /@ Range[Min[Length[zeck], Length[dualZeck]]], 2, 1]; 1 + Position[s, _?(# == 0 &)] // Flatten


CROSSREFS

Cf. A000045, A000931, A007895, A014417, A104326, A112310, A331466.
Sequence in context: A092360 A129141 A289013 * A337289 A097431 A123929
Adjacent sequences: A331464 A331465 A331466 * A331468 A331469 A331470


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, Jan 17 2020


STATUS

approved



