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A094709 Smallest k such that prime(n)# - k and prime(n)# + k are primes, where prime(n)# = A002110(n). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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 *)

PROG

(Python)

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

CROSSREFS

Cf. A078611, A002110, A094710, A094711.

Sequence in context: A037283 A278634 A306507 * A236231 A040181 A123187

Adjacent sequences: A094706 A094707 A094708 * A094710 A094711 A094712

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 21 2004

EXTENSIONS

More terms from Don Reble, May 27 2004

STATUS

approved

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Last modified February 5 12:47 EST 2023. Contains 360084 sequences. (Running on oeis4.)