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A094709
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Smallest k such that prime(n)# - k and prime(n)# + k are primes, where prime(n)# = A002110(n).
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3
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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
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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David Wasserman, Table of n, a(n) for n = 1..250
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EXAMPLE
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a(4)=13 because prime(4)=7, 7# = 2*3*5*7 = 210, and 210 - 13 and 210 + 13 are primes.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A078611, A002110, A094710, A094711.
Sequence in context: A037283 A278634 A306507 * A236231 A040181 A123187
Adjacent sequences: A094706 A094707 A094708 * A094710 A094711 A094712
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, May 21 2004
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EXTENSIONS
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More terms from Don Reble, May 27 2004
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STATUS
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approved
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