A094710 Smaller of a pair (p,q) of primes with (p+q)/2=prime(n)# and q-p is minimal.

5, 29, 197, 2309, 30013, 510451, 9699667, 223092791, 6469693129, 200560490047, 7420738134571, 304250263527139, 13082761331669881, 614889782588491043, 32589158477190044657, 1922760350154212638159, 117288381359406970982957, 7858321551080267055878717, 557940830126698960967414867

Offset: 2

Author

Reinhard Zumkeller, May 21 2004

Keywords

• nonn

Comments

a(n) = Max{p prime: (p+q)/2=prime(n)# for another prime q>p};

a(n) = A002110(n) - A094709(n); (a(n) + A094711(n))/2 = A002110(n).

Crossrefs

Cf. A002110, A094709, A094711.

Programs

Python

from sympy import isprime, prime, primerange
def aupton(terms):
  phash, alst = 2, []
  for p in primerange(3, prime(terms)+1):
    phash *= p
    for k in range(1, phash//2):
      if isprime(phash-k) and isprime(phash+k): alst.append(phash-k); break
  return alst
print(aupton(20)) # Michael S. Branicky, May 29 2021

Extensions

Corrected by T. D. Noe, Nov 15 2006

a(12)-a(20) from Donovan Johnson, Apr 27 2008