A374610 - OEIS

%I #26 Jul 28 2024 00:19:52

%S 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,

%T 53,74,71,78,77,79,125,80,131,133,149,134,155,152,159,158,160,206,161,

%U 212,214,230,215,236,233,240,239,241,401,242,449,404,455,457,473

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

%C 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.

%C Among possible representations, a(n) is the smallest a(n) = Sum_{i} d_i * 3^i.

%C 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.

%e For n = 3, 3 = 1*3 + 0*2 = 10_p => 10_3 = 1*3 + 0*1 = 3_10 = a(3).

%e For n = 5, 5 = 1*3 + 1*2 = 11_p => 11_3 = 1*3 + 1*1 = 4_10 = a(5).

%e 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).

%K nonn

%O 2,2

%A _Kaleb Williams_, Jul 13 2024