A309261 - OEIS

%I #20 Aug 11 2019 01:40:17

%S 0,0,1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,0,10,12,3,1,3,2,2,3,3,4,1,4,2,

%T 4,3,5,1,5,2,5,3,6,1,6,2,6,3,7,1,7,2,7,3,8,1,8,2,8,3,9,1,9,2,9,3,10,

%U 22,10,24,16,16,18,18,20,27,18,22,15,21,35,16,25,24,24

%N The sum of the number of times each unique digit in the previous number occurred in the numbers before that with a(1) = 0.

%H Rémy Sigrist, <a href="/A309261/b309261.txt">Table of n, a(n) for n = 1..20000</a>

%H Rémy Sigrist, <a href="/A309261/a309261.png">Density plot of the first million terms</a>

%e For n=2, the previous term a(1) is 0 by definition and the digit 0 has never been seen before so a(2) is 0.

%e For n=3, a(2) is 0, the digit 0 has been seen once before so a(3) is 1.

%e For n=22, a(21) is 10, digit 1 has been seen once before a(21) and digit 0 has been seen eleven times, so a(22) = 12.

%e For n=68, a(67) is 22, digit 2 has been seen ten times before, we only consider unique digits of a(n-1), so a(68) = 10.

%o (PARI) { f=vector(base=10); for(n=1, 84, if(n==1, v=0, d=if(v, digits(v, base), [0]); s=Set(d); v=sum(i=1, #s, f[1+s[i]]); apply(t -> f[1+t]++, d)

%o ); print1(v ", ")) } \\ _Rémy Sigrist_, Jul 24 2019

%Y Cf. A004207.

%K nonn,base

%O 1,5

%A _Nic Tomlinson_, Jul 19 2019