A349793 Primes which are the nearest integer to the harmonic mean of the previous prime and the following prime.

3, 7, 13, 23, 47, 89, 157, 173, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903, 2963, 3307, 3313, 3637, 3733, 4013, 4409, 4457, 4597, 4657, 4691, 4993, 5107, 5113, 5303, 5387, 5393

Offset: 1

Author

Hugo Pfoertner, Nov 30 2021

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006562, A046869, A051635, A075540, A216124.

Programs

Mathematica

Select[Partition[Prime[Range[750]],3,1],Round[HarmonicMean[{#[[1]],#[[3]]}]]==#[[2]]&][[;;,2]] (* Harvey P. Dale, Dec 29 2024 *)

PARI

a349793(limit) = {my(p1=2,p2=3); forprime(p3=5, limit, my(hm=round((2*p1*p3)/(p1+p3))); if(p2==hm, print1(p2,", ")); p1=p2;p2=p3)};
a349793(5500)