A387170 Self-inventory sequence modulo 10: start with 0; repeatedly append the counts of digits 0..9 seen so far, taken mod 10.

0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 2, 1, 0, 0, 0, 0, 0, 0, 1, 5, 4, 1, 0, 1, 1, 0, 0, 0, 1, 9, 8, 1, 0, 1, 1, 0, 0, 1, 2, 2, 2, 4, 0, 2, 1, 0, 0, 1, 2, 5, 4, 6, 0, 3, 2, 1, 0, 1, 2, 7, 6, 8, 1, 3, 2, 2, 1, 2, 2, 7, 8, 2, 2, 3, 2, 2, 2, 3, 2, 7, 8, 8, 4, 4, 2, 2, 3, 5, 2, 7, 8, 1, 5, 5, 5

Offset

0,12

Comments

Empirical: The sequence begins to repeat starting at n = 280730 (offset 0) with a period of 63140. That is, for all n >= 280730 we have a(n) = a(n+63140). The repeating block beginning at n = 280730 is (9,9,6,3,8,3,3,4,8,1,1,...).

Empirical: There is exactly one occurrence of a run of 7 consecutive terms with successive differences -1. It starts at n = 16701 and is (7,6,5,4,3,2,1). There are no increasing runs of 7 consecutive terms, and are no runs of length >= 8.

Empirical: The first occurrence of a run of 5 constant values past the initial repeating zeros (that is, beginning with n > 15) starts at n = 8334 and is five 6's in a row. There are no runs of length >= 6 of constant values beginning with n > 14.

Links

Cameron Johnson, Table of n, a(n) for n = 0..9999

Example

Start with a(0) = 0;
then we append the count of digits 0 seen so far (mod 10): one 0 -> a(1) = 1;
then we append the count of digits 1 seen so far (mod 10): one 1 -> a(2) = 1;
then we append the count of digits 2 seen so far (mod 10): zero 2s -> a(3) = 0;
..
then we append the count of digits 9 seen so far (mod 10): zero 9s -> a(10) = 0;
then we append the count of digits 0 seen so far (mod 10): nine 0s -> a(11) = 9;
then we append the count of digits 1 seen so far (mod 10): two 1s -> a(12) = 2;
then we append the count of digits 2 seen so far (mod 10): one 2 -> a(13) = 1;
etc.

Maple

P:=proc(q) local n, v; v:=[0]; for n from 1 to q do
v:=[op(v), numboccur((n-1) mod 10, v) mod 10]; od; op(v); end: P(10^2); Paolo P. Lava, Aug 21 2025

Prog

(JavaScript)
// To generate the first 280730 pre-periodic terms:
var base = 10;
var size = 280730;
var iterations = Math.floor(size/base);
var a = Array(size);
a[0] = 0;
var inventory = Array(base).fill(0);
inventory[0] = 1;
var n = 1;
for (var i = 0; i < iterations; i++) {
  for (var target = 0; target < base && n < size; target++, n++) {
    var count = inventory[target] % base;
    inventory[count]++;
    a[n] = count;
  }
}
(Python)
from itertools import islice
def agen(): # generator of terms
    inventory = [1] + [0]*9
    yield 0
    while True:
        for i in range(10):
            yield (c:=inventory[i]%10)
            inventory[c%10] += 1
print(list(islice(agen(), 97))) # Michael S. Branicky, Aug 20 2025

Crossrefs

Cf. A342585.

Sequence in context: A240985 A296460 A379587 * A319533 A010160 A093962

Adjacent sequences: A387167 A387168 A387169 * A387171 A387172 A387173

Keyword

nonn

Author

Cameron Johnson, Aug 20 2025

Status

approved