A112763 Smallest prime factor of the n-th 5-smooth number.

1, 2, 3, 2, 5, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 5, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3

Offset

1,2

Links

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

Formula

a(n) = A020639(A051037(n));

a(n) <= A112764(n) <= 5.

a(A188427(n)) = 5 for n > 1. - David A. Corneth, Feb 07 2020

Mathematica

FactorInteger[#][[1, 1]] & /@ Select[Range[3000], Last @ Map[First, FactorInteger[#]] <= 5 &] (* Amiram Eldar, Feb 07 2020 *)

Prog

(Magma) [1] cat [Min(PrimeDivisors(k)): k in [2..1500]| PrimeDivisors(k) subset [2, 3, 5]]; // Marius A. Burtea, Feb 07 2020
(Python)
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A112763(n):
    if n == 1: return 1
    def f(x):
        c = n+x
        i, i5 = 0, 1
        while i5<=x:
            j, j3 = 0, 1
            y = x//i5
            z = y
            while j3 <= y:
                c -= z.bit_length()
                j += 1
                j3 *= 3
                z //= 3
            i += 1
            i5 *= 5
        return c
    return 2 if not (m:=bisection(f, n, n))&1 else 5 if 5**integer_log(m, 5)[0]==m else 3 # Chai Wah Wu, Mar 12 2026

Crossrefs

Cf. A020639, A051037, A086410, A112755, A112764, A188425, A188426, A188427.

Sequence in context: A124386 A098668 A387025 * A093476 A262597 A217607

Adjacent sequences: A112760 A112761 A112762 * A112764 A112765 A112766

Keyword

nonn

Author

Reinhard Zumkeller, Sep 18 2005

Status

approved