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A374610
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Smallest result of n in "base-p" using digits 0,1,2 and interpreted as base-3.
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0
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1, 3, 2, 4, 6, 5, 7, 11, 8, 15, 14, 16, 20, 17, 24, 23, 25, 41, 26, 47, 44, 51, 50, 52, 68, 53, 74, 71, 78, 77, 79, 125, 80, 131, 133, 149, 134, 155, 152, 159, 158, 160, 206, 161, 212, 214, 230, 215, 236, 233, 240, 239, 241, 401, 242, 449, 404, 455, 457, 473
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OFFSET
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2,2
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COMMENTS
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A "base-p" representation of n is n = Sum_{i} d_i * prime(i+1) with i >= 0 and with "digits" 0 <= d_i <= 2.
Among possible representations, a(n) is the smallest a(n) = Sum_{i} d_i * 3^i.
The effect is to the lazy representation of n as the sum of up to 2 of each prime, with lazy meaning work from largest to smallest prime and use the fewest of each as long as smaller primes will be sufficient to complete the sum.
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LINKS
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EXAMPLE
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For n = 3, 3 = 1*3 + 0*2 = 10_p => 10_3 = 1*3 + 0*1 = 3_10 = a(3).
For n = 5, 5 = 1*3 + 1*2 = 11_p => 11_3 = 1*3 + 1*1 = 4_10 = a(5).
For n = 19, 19 = 1*7 + 1*5 + 1*3 + 2*2 = 1112_p => 1112_3 = 1*27 + 1*9 + 1*3 + 2*1 = 41_10 = a(19).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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