A280870 Numerator of the mediant of prime(n) / prime(n+1) and prime(n+2) / prime(n+3).

7, 5, 4, 5, 7, 4, 5, 8, 9, 11, 9, 10, 11, 48, 53, 19, 21, 33, 14, 25, 13, 14, 18, 19, 25, 52, 53, 55, 59, 61, 44, 135, 143, 145, 153, 157, 27, 168, 173, 177, 185, 187, 97, 49, 204, 211, 219, 113, 115, 78, 237, 245, 249, 257, 263, 89, 91, 69, 40, 287, 295

Offset

1,1

Comments

The mediant of two reduced proper fractions a/b and c/d is (a+c)/(b+d), the value of which is strictly between a/b and c/d.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Wikipedia, Mediant

Example

The mediant of 2/3 and 5/7 is 7/10.

Mathematica

Array[Numerator[(#1 + #3)/(#2 + #4)] & @@ Prime@ Range[#, # + 3] &, 61] (* Michael De Vlieger, Oct 08 2021 *)

Prog

(PARI) vector(100, n, numerator((prime(n)+prime(n+2)) / (prime(n+1)+prime(n+3))))
(Python)
from math import gcd
from sympy import nextprime
def aupton(terms):
    alst, p, q, r, s = [], 2, 3, 5, 7
    while len(alst) < terms:
        alst.append((p+r)//gcd(p+r, q+s))
        p, q, r, s = q, r, s, nextprime(s)
    return alst
print(aupton(61)) # Michael S. Branicky, Oct 08 2021

Crossrefs

Cf. A000040, A280871.

Sequence in context: A273841 A112407 A154195 * A019858 A289032 A289005

Adjacent sequences: A280867 A280868 A280869 * A280871 A280872 A280873

Keyword

nonn,frac

Author

Colin Barker, Jan 09 2017

Status

approved