A094711 -id:A094711 - cp's OEIS frontend

A094709 Smallest k such that prime(n)# - k and prime(n)# + k are primes, where prime(n)# = A002110(n).

0, 1, 1, 13, 1, 17, 59, 23, 79, 101, 83, 239, 71, 149, 367, 73, 911, 313, 373, 523, 313, 331, 197, 101, 1493, 523, 293, 577, 2699, 1481, 1453, 5647, 647, 419, 757, 4253, 509, 239, 10499, 191, 4013, 2659, 617, 6733, 1297, 971

Offset: 1

Reinhard Zumkeller, May 21 2004

nonn

a(n) = A002110(n) - A094710(n) = A094711(n) - A002110(n),

Goldbach's conjecture implies that a(n) is defined for all n. - David Wasserman, May 31 2007

			a(4)=13 because prime(4)=7, 7# = 2*3*5*7 = 210, and 210 - 13 and 210 + 13 are primes.

David Wasserman, Table of n, a(n) for n = 1..250

Cf. A078611, A002110, A094710, A094711.

pc[n_]:=Module[{x=0,i=0},Do[If[PrimeQ[n-i]&&PrimeQ[n+i],x=i;Break[]],{i,9!}];x]; r=2;lst={};Do[p=Prime[n];r*=p;AppendTo[lst,pc[r]],{n,2,2*4!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
sk[n_]:=Module[{k=0},While[!PrimeQ[n+k]||!PrimeQ[n-k],k++];k]; sk/@ FoldList[ Times,Prime[Range[50]]] (* Harvey P. Dale, Apr 03 2022 *)

from sympy import isprime, prime, primerange
def aupton(terms):
  phash, alst = 2, [0]
  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(k); break
  return alst
print(aupton(46)) # Michael S. Branicky, May 29 2021

More terms from Don Reble, May 27 2004

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

Original entry on oeis.org

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

Offset: 2

Reinhard Zumkeller, May 21 2004

nonn

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).

Cf. A002110, A094709, A094711.

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

Corrected by T. D. Noe, Nov 15 2006

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

cp's OEIS Frontend

A094709 Smallest k such that prime(n)# - k and prime(n)# + k are primes, where prime(n)# = A002110(n).

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