A309261 The sum of the number of times each unique digit in the previous number occurred in the numbers before that with a(1) = 0.

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

Offset

1,5

Links

Rémy Sigrist, Table of n, a(n) for n = 1..20000

Rémy Sigrist, Density plot of the first million terms

Example

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

Prog

(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)
); print1(v ", ")) } \\ Rémy Sigrist, Jul 24 2019

Crossrefs

Cf. A004207.

Sequence in context: A276457 A171181 A364788 * A326834 A034948 A135472

Adjacent sequences: A309258 A309259 A309260 * A309262 A309263 A309264

Keyword

nonn,base

Author

Nic Tomlinson, Jul 19 2019

Status

approved