A375078 a(1)=1; thereafter a(n) is the number of digits in (n mod 10) already present in the sequence.

1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 1, 0, 15, 4, 0, 0, 1, 1, 0, 0, 1, 0, 20, 7, 1, 0, 1, 1, 0, 1, 1, 0, 24, 12, 3, 1, 2, 1, 0, 1, 1, 0, 26, 17, 5, 1, 2, 2, 1, 2, 1, 0, 27, 21, 10, 1, 2, 2, 1, 3, 1, 0, 29, 26, 14, 2, 3, 2, 2, 3, 1, 1, 29, 29, 19

Offset

1,10

Links

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Paolo P. Lava, Digit charts for the first 20000 terms

Paolo P. Lava, First 1000 terms

Carlos Rivera, Puzzle 1182. Another sequence by Paolo Lava, The Prime Puzzles and Problems Connection.

Maple

P:=proc(q) local a, b, c, n; a:=[1]; b:=[1];
for n from 2 to q do c:=numboccur(n mod 10, b); a:=[op(a), c];
if c=0 then b:=[op(b), 0]; else b:=[op(b), op(convert(c, base, 10))]; fi; od;
print(op(a)); end: P(10^3);

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    s = "1"
    yield 1
    for n in count(2):
        an = s.count(str(n%10))
        s += str(an)
        yield an
print(list(islice(agen(), 82))) # Michael S. Branicky, Aug 02 2024
(Python)
from collections import Counter
def A375078_gen(): # generator of terms
    c, n = Counter({1:1}), 1
    yield 1
    while True:
        n = (n+1)%10
        yield c[n]
        c += Counter(map(int, str(c[n])))
A375078_list = list(islice(A375078_gen(), 30)) # Chai Wah Wu, Aug 03 2024

Crossrefs

Cf. A136706-A136714.

Sequence in context: A076107 A076952 A209914 * A365237 A342980 A379386

Adjacent sequences: A375075 A375076 A375077 * A375079 A375080 A375081

Keyword

nonn,base,easy

Author

Paolo P. Lava, Jul 29 2024

Status

approved