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Search: id:A114141
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| A114141 |
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Difference between first odd semiprime > 3^n and 3^n. |
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+0
1
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| 8, 6, 6, 6, 4, 4, 2, 2, 22, 6, 8, 2, 2, 20, 10, 4, 6, 8, 4, 4, 2, 4, 20, 10, 8, 6, 28, 2, 2, 8, 14, 12, 20, 10, 14, 20, 16, 6, 14, 4, 2, 8, 8, 12, 2, 24, 20, 10, 10, 4, 48
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A098147 is difference between first odd semiprime > 10^n and 10^n. How can we prove that there exists an a(n) for all n? In this powers of 3 sequence, does 2 occur infinitely often? Does every even integer k > 0 occur?
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FORMULA
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a(n) = minimum integer k such that 3^n + k is an element of A046315. a(n) = minimum integer k such that A000244(n) + k is an element of A046315.
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EXAMPLE
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a(0) = 8 because 3^0 + 8 = 9 = 3^2 is an odd semiprime.
a(1) = 6 because 3^1 + 6 = 9 = 3^2 is an odd semiprime.
a(2) = 6 because 3^2 + 6 = 15 = 3 * 5 is an odd semiprime.
a(3) = 6 because 3^3 + 6 = 33 = 3 * 11 is an odd semiprime.
a(4) = 4 because 3^4 + 4 = 85 = 5 * 17 is an odd semiprime.
a(5) = 4 because 3^5 + 4 = 247 = 13 * 19 is an odd semiprime.
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CROSSREFS
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Cf. A000244, A001358, A098147.
Sequence in context: A067970 A003675 A121948 this_sequence A089139 A093209 A154499
Adjacent sequences: A114138 A114139 A114140 this_sequence A114142 A114143 A114144
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 03 2006
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