A390028 Record denominators of (p2-1)/(p1-1), where p1 < p2 are consecutive primes.

1, 2, 3, 5, 8, 9, 11, 14, 20, 21, 23, 26, 29, 33, 35, 39, 41, 50, 51, 53, 63, 65, 68, 69, 74, 81, 83, 86, 89, 95, 98, 111, 113, 116, 119, 125, 128, 131, 134, 140, 141, 146, 153, 155, 158, 168, 173, 176, 179, 189, 191, 204, 209, 215, 219, 221, 230, 231, 233, 239, 243

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

           s    t        denominator
  p1  p2 p2-1 p1-1  s/t  (s/t)
   2   3   2    1   2/1    1 = a(1)
   3   5   4    2   2/1    1
   5   7   6    4   3/2    2 = a(2)
   7  11  10    6   5/3    3 = a(3)
  11  13  12   10   6/5    5 = a(4)
  13  17  16   12   4/3    3
  17  19  18   16   9/8    8 = a(5)
  19  23  22   18  11/9    9 = a(6)
  23  29  28   22  14/11  11 = a(7)
  29  31  30   28  15/14  14 = a(8)
  31  37  36   30   6/5    5
  37  41  40   36  10/9    9
  41  43  42   40  21/20  20 = a(9)
  43  47  46   42  23/21  21 = a(10)

Prog

(Python)
from itertools import islice
from math import gcd
from sympy import nextprime
def A390028_gen(): # generator of terms
    c, p, q = 0, 2, 3
    while True:
        if (d:=(p-1)//gcd(p-1, q-1))>c:
            yield d
            c = d
        p, q = q, nextprime(q)
A390028_list = list(islice(A390028_gen(), 61)) # Chai Wah Wu, Oct 24 2025

Crossrefs

Cf. A390027, A390098, A390099.

Sequence in context: A119863 A285253 A047254 * A226815 A284890 A051214

Adjacent sequences: A390025 A390026 A390027 * A390029 A390030 A390031

Keyword

nonn

Author

Hugo Pfoertner, Oct 22 2025

Status

approved