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A374610
Smallest result of n in "base-p" using digits 0,1,2 and interpreted as base-3.
0
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
OFFSET
2,2
COMMENTS
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.
EXAMPLE
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).
CROSSREFS
Sequence in context: A166695 A254107 A116942 * A254108 A093573 A126290
KEYWORD
nonn
AUTHOR
Kaleb Williams, Jul 13 2024
STATUS
approved