A343644 a(n) is the sum of the number of occurrences of each digit of n up to and including that digit.

1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 7, 8, 9, 10, 11, 12, 13, 14, 5, 17, 11, 10, 11, 12, 13, 14, 15, 16, 7, 19, 20, 15, 13, 14, 15, 16, 17, 18, 9, 21, 22, 23, 19, 16, 17, 18, 19, 20, 11, 23, 24, 25, 26, 23, 19, 20, 21, 22, 13, 25, 26, 27, 28, 29, 27, 22, 23, 24, 15, 27

Offset

1,10

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

a(10) = 3 as the digit 1 is the second digit 1 and the digit 0 is the first digit 0 giving 2+1.
a(22) is 11 as the digits of 22 are 2 and 2. Before 22 the digit 2 occurred four times, in 2, 12, 20 in 21. The first 2 in 22 is the fifth in total. The second 2 in 22 is the sixth 2 in total giving 5 + 6.

Mathematica

Array[Sum[Count[Flatten@Join[IntegerDigits/@Range[#-1], a[[;; k]]], a[[k]]], {k, Length[a=IntegerDigits@#]}]&, 100] (* Giorgos Kalogeropoulos, Apr 23 2021 *)

Prog

(PARI) first(n) = my(v=vector(10), res=vector(n)); for(i=1, n, c=0; d=digits(i); for(i=1, #d, v[d[i]+1]++; c+=v[d[i]+1]); res[i]=c); res
(Python)
def aupto(limit):
  f, alst = [0 for i in range(10)], []
  for n in range(1, limit+1):
    s = 0
    for d in list(map(int, str(n))): f[d] += 1; s += f[d]
    alst.append(s)
  return alst
print(aupto(71)) # Michael S. Branicky, Apr 23 2021

Crossrefs

Cf. A343645.

Sequence in context: A325894 A370517 A176269 * A081522 A020764 A010625

Adjacent sequences: A343641 A343642 A343643 * A343645 A343646 A343647

Keyword

nonn,easy,base,look

Author

David A. Corneth, Apr 23 2021

Status

approved