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A358847
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a(n) = 1 if A053669(6*n) [the smallest prime not dividing 6*n] is of the form 6m-1, otherwise a(n) = 0.
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5
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1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0
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OFFSET
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1
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 6 * Sum_{p prime, p == 5 (mod 6)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.8261626908... . - Amiram Eldar, Apr 16 2024
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EXAMPLE
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For n = 85085 = 5*7*11*13*17, 6*n = A002110(7) = 510510, whose smallest nondividing prime is 19, which is of the form 6m+1, therefore a(85085) = 0.
For n = 1616615 = 5*7*11*13*17*19, 6*n = A002110(8), whose smallest nondividing prime is 23, which is of the form 6m-1, therefore a(1616615) = 1.
For n = 37182145 = 5*7*11*13*17*19*23, 6*n = A002110(9), whose smallest nondividing prime is 29, which is of the form 6m-1, therefore a(37182145) = 1. This is the first case where the alternating pattern following A276084 breaks.
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PROG
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(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p)));
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CROSSREFS
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Characteristic function of A358849, whose complement A358848 gives the positions of zeros.
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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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