A112755 Smallest prime factor of n-th number of the form 3^i*5^j.

1, 3, 5, 3, 3, 5, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A020639(A003593(n));

a(n) <= A112756(n) <= 5.

Mathematica

s = {}; m = 12; Do[n = 5^k; While[n <= 5^m, AppendTo[s, n]; n *= 3], {k, 0, m}]; FactorInteger[#][[1, 1]] & /@ Union[s] (* Amiram Eldar, Feb 07 2020 *)

Prog

(Python)
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A112755(n):
    if n == 1: return 1
    def f(x): return n+x-sum(integer_log(x//5**i, 3)[0]+1 for i in range(integer_log(x, 5)[0]+1))
    return 3+(bool(bisection(f, n, n)%3)<<1) # Chai Wah Wu, Mar 13 2026

Crossrefs

Cf. A003593, A020639, A086410, A112756, A112763.

Sequence in context: A225581 A275391 A092553 * A284721 A126659 A246917

Adjacent sequences: A112752 A112753 A112754 * A112756 A112757 A112758

Keyword

nonn

Author

Reinhard Zumkeller, Sep 18 2005

Status

approved