A112752 Greatest common divisors of consecutive terms of numbers of the form 3^i*5^j.

1, 1, 1, 3, 5, 1, 9, 15, 3, 1, 5, 45, 9, 3, 15, 5, 25, 27, 9, 45, 15, 75, 81, 1, 125, 135, 45, 225, 243, 3, 375, 405, 5, 625, 675, 729, 9, 1125, 1215, 15, 1875, 2025, 2187, 1, 3125, 3375, 3645, 45, 5625, 6075, 6561, 3, 9375, 10125, 10935, 5, 15625, 16875, 18225

Offset

1,4

Links

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

Formula

a(n) = gcd(A003593(n), A003593(n+1)).

Mathematica

s = {}; m = 12; Do[n = 5^k; While[n <= 5^m, AppendTo[s, n]; n *= 3], {k, 0, m}]; Map[GCD @@ # &, Partition[Union[s], 2, 1]] (* Amiram Eldar, Feb 06 2020 *)

Prog

(Python)
from math import gcd
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A112752(n):
    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 gcd(m:=bisection(f, n, n), bisection(lambda x:f(x)+1, m, m)) # Chai Wah Wu, Mar 09 2026

Crossrefs

Cf. A003593, A112757.

Sequence in context: A054586 A214229 A214728 * A101035 A204029 A026253

Adjacent sequences: A112749 A112750 A112751 * A112753 A112754 A112755

Keyword

nonn

Author

Reinhard Zumkeller, Sep 18 2005

Status

approved