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A191106
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Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 3x are in a.
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15
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1, 3, 7, 9, 19, 21, 25, 27, 55, 57, 61, 63, 73, 75, 79, 81, 163, 165, 169, 171, 181, 183, 187, 189, 217, 219, 223, 225, 235, 237, 241, 243, 487, 489, 493, 495, 505, 507, 511, 513, 541, 543, 547, 549, 559, 561, 565, 567, 649, 651, 655, 657, 667, 669, 673, 675, 703, 705, 709, 711, 721, 723, 727, 729, 1459, 1461, 1465, 1467, 1477
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OFFSET
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1,2
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COMMENTS
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Related sequences for various choices of i and k as defined in A190803:
For a=A191106, we have closure properties: the integers in (2+a)/3 comprise a; the integers in a/3 comprise a.
For k >= 1, m = a(i), 1 <= i <= 2^k seems to be m such that m/(3^k+1) is in the Cantor set (except that m = 0 and m = 3^k+1 do not appear). For k >= 2, m = (a(i)-1)/2, 1 <= i <= 2^k seems to be m such that m/((3^k-1)/2) is in the Cantor set. - Peter Munn, Jul 06 2019
Every even number is the sum of two (possibly equal) terms. More specifically: terms a(1) through a(2^n) = 3^n sum to even numbers 2 times 1 through 3^n. Every even number is infinitely often the difference of two terms. Since the sequence is equal to 2*A005836(n) + 1, these properties follow immediately from similar properties of A005836 for every number. - Aad Thoen, Feb 17 2022
if A_n=(a(1),a(2),...,a(2^n)), then A_(n+1)=(A_n,A_n+2*3^n), similar to A003278. - Arie Bos, Jul 26 2022
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LINKS
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FORMULA
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EXAMPLE
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1 -> 3 -> 7,9 -> 19,21,25,27 -> ...
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MATHEMATICA
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h = 3; i = -2; j = 3; k = 0; f = 1; g = 9;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]] (* A191106; regarding g, see note at A190803 *)
b = (a + 2)/3; c = a/3; r = Range[1, 900];
d = Intersection[b, r](* illustrates closure property *)
e = Intersection[c, r](* illustrates closure property *)
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CROSSREFS
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Similar formula as A003278, A_(n+1)=(A_n,A_n+2*3^n).
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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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