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 A084088 Numbers k such that k == 2 (mod 3) and the exponent of the highest power of 2 dividing k is even. 4
 5, 11, 17, 20, 23, 29, 35, 41, 44, 47, 53, 59, 65, 68, 71, 77, 80, 83, 89, 92, 95, 101, 107, 113, 116, 119, 125, 131, 137, 140, 143, 149, 155, 161, 164, 167, 173, 176, 179, 185, 188, 191, 197, 203, 209, 212, 215, 221, 227, 233, 236, 239, 245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers that are both in A016789 and A003159. 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). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Index entries for 2-automatic sequences. MATHEMATICA Select[3 * Range[0, 81] + 2, EvenQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 16 2022 *) PROG (PARI) for(n=0, 300, if(valuation(n, 2)%2==0&&n%3==2, print1(n", "))) (Python) from itertools import count, islice def A084088_gen(): # generator of terms return filter(lambda n:(n&-n).bit_length()&1, count(2, 3)) A084088_list = list(islice(A084088_gen(), 30)) # Chai Wah Wu, Jul 11 2022 CROSSREFS Intersection of A016789 and A003159. Cf. A084091. A352273 without the multiples of 9. Sequence in context: A179240 A176905 A352273 * A344160 A314183 A314184 Adjacent sequences: A084085 A084086 A084087 * A084089 A084090 A084091 KEYWORD nonn,easy AUTHOR Ralf Stephan, May 11 2003 STATUS approved

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Last modified November 29 19:18 EST 2023. Contains 367447 sequences. (Running on oeis4.)