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A160217
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Minimal increasing sequence with a(1)=3 and the property that a(n) and n are both in or both not in A003159.
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5
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3, 6, 7, 9, 11, 14, 15, 18, 19, 22, 23, 25, 27, 30, 31, 33, 35, 38, 39, 41, 43, 46, 47, 50, 51, 54, 55, 57, 59, 62, 63, 66, 67, 70, 71, 73, 75, 78, 79, 82, 83, 86, 87, 89, 91, 94, 95, 97, 99, 102, 103, 105, 107, 110, 111, 114, 115, 118, 119, 121, 123, 126, 127, 129, 131, 134
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OFFSET
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1,1
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COMMENTS
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The primes in this sequence give A160216.
Conjecture: Let m>3 belong to A003159. Define the sequence b(n) to be the minimal increasing sequence with b(1)=m and the property that b(n) and n are both in or both not in A003159. Then a(n)=b(n) for all n larger than some m-dependent minimum index.
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LINKS
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FORMULA
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EXAMPLE
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n=2 is not in A003159. So a(2) is the smallest number larger than a(1)=3 which is not in A003159. This excludes 4 and 5 which are in A003159 and leads to a(2)=6.
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MATHEMATICA
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a35263[n_] := 1 - Mod[IntegerExponent[n, 2], 2];
a[1] = 3; a[n_] := a[n] = For[k = a[n - 1] + 1, True, k++, If[a35263[k] == a35263[n], Return[k]]];
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PROG
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(PARI) is(n) = valuation(n, 2)%2==0; \\ A003159
nexta(a, n) = {my(k=a+1, isn = is(n)); while (is(k) != isn, k++); k; };
lista(nn) = {my(a = 3); print1(a, ", "); for (n=2, nn, a = nexta(a, n); print1(a, ", "); ); } \\ Michel Marcus, Dec 15 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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