A393574 Lesser of two consecutive 5-smooth numbers that are coprime.

1, 2, 3, 4, 5, 8, 9, 15, 24, 25, 80, 125, 128, 243, 2025, 3072, 15552, 16384, 19683, 32768, 78125, 390625, 1594323, 66430125, 128000000, 1220703125, 4271484375, 6103515625, 10460353203, 31250000000, 274658203125, 7625597484987, 19042491875328, 9007199254740992

Offset

1,2

Comments

Subsequence of A051037 \ A143207. - Chai Wah Wu, Mar 11 2026

Links

Chai Wah Wu, Table of n, a(n) for n = 1..86 (terms 1..72 from Michael De Vlieger)

Example

Let s = A051037 and b = A393575.
Table of n, a(n), and b(n) for select n:
 n             a(n)               b(n)
---------------------------------------------------
 1     s(1) =    1 = 1              2 = 2
 2     s(2) =    2 = 2              3 = 3
 3     s(3) =    3 = 3              4 = 2^2
 4     s(4) =    4 = 2^2            5 = 5
 5     s(5) =    5 = 5              6 = 2    * 3
 6     s(7) =    8 = 2^3            9 = 3^2
10    s(16) =   25 = 5^2           27 = 3^3
11    s(30) =   80 = 2^4 * 5       81 = 3^4
12    s(37) =  125 = 5^3          128 = 2^7
13    s(38) =  128 = 2^7          135 = 3^3  * 5
14    s(50) =  243 = 3^5          250 = 2    * 5^3
15   s(109) = 2025 = 3^4 * 5^2   2048 = 2^11

Mathematica

nn = 2^10; s = Union@ Flatten@ Table[2^a * 3^b * 5^c, {a, 0, nn}, {b, 0, Log[3, nn/2^a]}, {c, 0, Log[5, nn/(2^a*3^b)] } ]; Select[Partition[s, 2, 1], CoprimeQ @@ # &][[;; , 1]]

Prog

(Python) # uses code in A051037
from math import gcd
from itertools import islice, pairwise
def agen(): yield from (a for a, b in pairwise(A051037gen()) if gcd(a, b) == 1)
print(list(islice(agen(), 34))) # Michael S. Branicky, Feb 22 2026

Crossrefs

Cf. A051037, A186712, A186927, A393575, A143207.

Sequence in context: A054168 A301464 A354829 * A085152 A392740 A264886

Adjacent sequences: A393571 A393572 A393573 * A393575 A393576 A393577

Keyword

nonn

Author

Michael De Vlieger, Feb 22 2026

Status

approved