A392635 7-smooth numbers k such that k / (next 7-smooth number after k) reaches a record large value.

1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 20, 24, 27, 35, 48, 49, 63, 80, 125, 224, 2400, 4374, 250000, 78121827, 205885750000000, 2251783932057135, 363797880709171295166015625, 37252879910233655318543787489, 639471113830161648869830843378434048, 386856165263818792142417337638583138065421

Offset

1,2

Links

Zhicheng Wei, Table of n, a(n) for n = 1..35

Example

From Michael De Vlieger, Feb 20 2026: (Start)
Let s = A002473 and let facs(x) represent the standard form prime decomposition of x.
Table of n, a(n) = s(i) for select n:
  n         i    a(n)  facs(a(n))      facs(s(i+1))
 --------------------------------------------------------
  1         1      1   1               2
  2         2      2   2               3
  3         3      3   3               2^2
  4         4      4   2^2             5
  5         5      5   5               2 * 3
 12        16     20   2^2 * 5         3 * 7
 13        18     24   2^3 * 3         5^2
 14        20     27   3^3             2^2 * 7
 21        70    224   2^5 * 7         3^2 * 5^2
 22       201   2400   2^5 * 3 * 5^2   7^4
 28    289773          5^38            2^42 * 3^15 * 7^8
 32   7313064          2^193 * 3^6     5^5  * 7^68         (End)

Mathematica

(* First, load "regs" function from "Fast Mathematica programs" at A369609, then: *) Numerator@ Union@ FoldList[Max, Divide @@@ Partition[regs[210, 2^150], 2, 1] ] (* Michael De Vlieger, Feb 19 2026 *)

Prog

(Python) # uses A002473gen() in A002473
from itertools import islice
from fractions import Fraction
def agen():
    g = A002473gen(); k = next(g); record = 0
    while True:
        nextk = next(g); f = Fraction(k, nextk)
        if f > record: yield k; record = f
        k = nextk
print(list(islice(agen(), 30)))

Crossrefs

Cf. A002473, A085153. Starts with A085153.

Sequence in context: A393603 A079334 A085153 * A339111 A130010 A282765

Adjacent sequences: A392632 A392633 A392634 * A392636 A392637 A392638

Keyword

nonn

Author

Zhicheng Wei, Feb 19 2026

Status

approved