A351870 - OEIS

%I #6 Feb 25 2022 10:57:24

%S 0,1,2,3,4,5,6,7,8,9,10,11111111111,12,13,14,15,16,17,18,19,20,21,112,

%T 23,24,25,26,27,28,29,30,31,32,1113,34,35,36,37,38,39,40,41,42,43,224,

%U 45,46,47,48,49,50,51,52,53,54,111115,56,57,58,59,60,61,62

%N a(n) is the least k such that A351868(k) = n.

%H Rémy Sigrist, <a href="/A351870/a351870.gp.txt">PARI program</a>

%F a(n) <= A002275(n).

%e For n = 44:

%e - the number 44 could encode 1 or 2 runs of consecutive equal digits,

%e - for 1 run, we have the following possibilities:

%e        11111111111111111111111111111111111111111111 (44 1's)

%e        2222222222222222222222 (22 2's)

%e        44444444444 (11 4's)

%e - for 2 runs, we have the following possibilities:

%e        11114 (4 1's and then 1 4's)

%e        224 (2 2's and then 1 4's)

%e        111122 (4 1's and then 2 2's)

%e        422 (1 4's and then 2 2's)

%e        221111 (2 2's and then 4 1's)

%e        41111 (1 4's and then 4 1's)

%e - the least possibility is 224,

%e - so a(44) = 224.

%o (PARI) See Links section.

%Y Cf. A002275, A351868.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Feb 22 2022