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A084089
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Numbers k such that k == 1 (mod 3) and the exponent of the highest power of 2 dividing k is even.
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5
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1, 4, 7, 13, 16, 19, 25, 28, 31, 37, 43, 49, 52, 55, 61, 64, 67, 73, 76, 79, 85, 91, 97, 100, 103, 109, 112, 115, 121, 124, 127, 133, 139, 145, 148, 151, 157, 163, 169, 172, 175, 181, 187, 193, 196, 199, 205, 208, 211, 217, 220, 223, 229, 235
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OFFSET
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1,2
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COMMENTS
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It seems that lim_{n->oo} a(n)/n = 9/2. [This is true. The asymptotic density of this sequence is 2/9. - Amiram Eldar, Jan 16 2022]
Positions of +1 in the expansion of Sum_{k>=0} x^2^k/(1+x^2^k+x^2^(k+1)) (A084091).
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LINKS
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MATHEMATICA
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Select[3 * Range[0, 81] + 1, EvenQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 16 2022 *)
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PROG
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(PARI) for(n=0, 300, if(valuation(n, 2)%2==0&&n%3==1, print1(n", ")))
(Python)
from itertools import count, islice
def A084089_gen(): # generator of terms
return filter(lambda n:(n&-n).bit_length()&1, count(1, 3))
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CROSSREFS
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A352274 without the multiples of 3.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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