A390098 Record denominators of (p1+1)/(p2+1), where p1 < p2 are consecutive primes.

4, 7, 9, 10, 16, 19, 21, 22, 31, 34, 37, 40, 49, 51, 52, 55, 57, 64, 70, 76, 79, 82, 91, 96, 97, 99, 100, 115, 117, 121, 126, 136, 139, 141, 142, 147, 157, 159, 166, 169, 174, 175, 177, 187, 190, 199, 201, 205, 211, 216, 217, 220, 229, 231, 232, 262, 271, 274, 279

Offset

1,1

Links

Table of n, a(n) for n=1..59.

Example

           s    t   s/t  denominator
  p1  p2 p1+1 p2+1       (s/t)
   2   3   3    4   3/4    4 = a(1)
   3   5   4    6   2/3    3
   5   7   6    8   3/4    4
   7  11   8   12   2/3    3
  11  13  12   14   6/7    7 = a(2)
  13  17  14   18   7/9    9 = a(3)
  17  19  18   20   9/10  10 = a(4)
  19  23  20   24   5/6    6
  23  29  24   30   4/5    5
  29  31  30   32  15/16  16 = a(5)
  31  37  32   38  16/19  19 = a(6)
  37  41  38   42  19/21  21 = a(7)
  41  43  42   44  21/22  22 = a(8)
  43  47  44   48  11/12  12
  47  53  48   54   8/9    9
  53  59  54   60   9/10  10
  59  61  60   62  30/31  31 = a(9)

Prog

(Python)
from itertools import islice
from math import gcd
from sympy import nextprime
def A390098_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)
A390098_list = list(islice(A390098_gen(), 59)) # Chai Wah Wu, Oct 24 2025

Crossrefs

Cf. A390027, A390028, A390099.

Sequence in context: A396305 A153001 A010454 * A391799 A272015 A310941

Adjacent sequences: A390095 A390096 A390097 * A390099 A390100 A390101

Keyword

nonn

Author

Hugo Pfoertner, Oct 24 2025

Status

approved