A374610 Smallest result of n in "base-p" using digits 0,1,2 and interpreted as base-3.

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.

Links

Table of n, a(n) for n=2..61.

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

Adjacent sequences: A374607 A374608 A374609 * A374611 A374612 A374613

Keyword

nonn

Author

Kaleb Williams, Jul 13 2024

Status

approved