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A390027
Record denominators of (p1-1)/(p2-1), where p1 < p2 are consecutive primes.
3
2, 3, 5, 6, 9, 11, 14, 15, 21, 23, 26, 29, 30, 35, 36, 41, 44, 51, 53, 54, 65, 68, 69, 74, 75, 83, 86, 89, 90, 96, 99, 113, 114, 119, 120, 128, 131, 134, 135, 141, 146, 153, 155, 156, 165, 173, 174, 179, 183, 191, 194, 209, 210, 216, 221, 224, 231, 233, 239, 243
OFFSET
1,1
EXAMPLE
s t s/t denominator
p1 p2 p1-1 p2-1 (s/t)
2 3 1 2 1/2 2 = a(1)
3 5 2 4 1/2 2
5 7 4 6 2/3 3 = a(2)
7 11 6 10 3/5 5 = a(3)
11 13 10 12 5/6 6 = a(4)
13 17 12 16 3/4 4
17 19 16 18 8/9 9 = a(5)
19 23 18 22 9/11 11 = a(6)
23 29 22 28 11/14 14 = a(7)
29 31 28 30 14/15 15 = a(8)
31 37 30 36 5/6 6
37 41 36 40 9/10 10
41 43 40 42 20/21 21 = a(9)
43 47 42 46 21/23 23 = a(10)
PROG
(Python)
from itertools import islice
from math import gcd
from sympy import nextprime
def A390027_gen(): # generator of terms
c, p, q = 0, 2, 3
while True:
if (d:=(q-1)//gcd(p-1, q-1))>c:
yield d
c = d
p, q = q, nextprime(q)
A390027_list = list(islice(A390027_gen(), 60)) # Chai Wah Wu, Oct 24 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Oct 22 2025
STATUS
approved