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

Author

Kaleb Williams, Jul 13 2024

Keywords

• nonn

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.

Examples

			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).