A390099 Record denominators of (p2+1)/(p1+1), where p1 < p2 are consecutive primes.

3, 6, 7, 9, 15, 16, 19, 21, 30, 31, 36, 37, 45, 49, 51, 54, 55, 57, 69, 75, 76, 79, 90, 91, 96, 97, 99, 114, 115, 120, 121, 135, 136, 139, 141, 142, 156, 157, 159, 166, 169, 174, 175, 184, 187, 195, 199, 201, 210, 211, 216, 217, 225, 229, 231, 261, 262, 271, 274

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

count:= 1: Res:= 3: M:= 3:
q:= 3:
while count < 100 do
  p:= q; q:= nextprime(q);
  v:= denom((q+1)/(p+1));
  if v > M then
    M:= v; Res:= Res, v; count:= count+1;
  fi; od:
Res; # Robert Israel, Feb 15 2026

Prog

(Python)
from itertools import islice
from math import gcd
from sympy import nextprime
def A390099_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)
print(list(islice(A390099_gen(), 59))) # Chai Wah Wu, Oct 24 2025

Crossrefs

Cf. A390027, A390028, A390098.

Sequence in context: A023982 A189092 A287268 * A191187 A310134 A039591

Adjacent sequences: A390096 A390097 A390098 * A390100 A390101 A390102

Keyword

nonn

Author

Hugo Pfoertner, Oct 24 2025

Status

approved