A110764 a(1) = 1; a(n+1) is the number of distinct prime divisors of concatenation a(1), a(2), a(3), ..., a(n).

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

Offset

1,3

Links

Table of n, a(n) for n=1..85.

Example

a(1) = 1 (given).
a(2) = 0 (number of distinct prime divisors of 1).
a(3) = 2 (number of distinct prime divisors of 10); etc.

Mathematica

l = {1}; s = "1"; Do[k = ToExpression[s]; m = Length[FactorInteger[k]]; AppendTo[l, m]; s = s <> ToString[m], {n, 1, 100}]; Print[l] (* Ryan Propper, Oct 10 2005 *)

Prog

(Python)
from sympy import factorint
def aupton(terms):
    alst, astr = [1], "1"
    for n in range(2, terms+1):
        an = len(factorint(int(astr)))
        alst.append(an)
        astr += str(an)
    return alst
print(aupton(45)) # Michael S. Branicky, Dec 02 2021

Crossrefs

Cf. A110762, A110763.

Sequence in context: A251619 A030620 A348241 * A107901 A334236 A030423

Adjacent sequences: A110761 A110762 A110763 * A110765 A110766 A110767

Keyword

base,nonn

Author

Amarnath Murthy, Aug 11 2005

Extensions

More terms from Ryan Propper, Oct 10 2005

Definition corrected by N. J. A. Sloane, Oct 14 2020 at the suggestion of David James Sycamore

a(71)-a(85) from Michael S. Branicky, Dec 02 2021

Status

approved