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 A078611 Radius of the shortest interval (of positive length) centered at prime(n) that has prime endpoints. 15
 2, 4, 6, 6, 6, 12, 6, 12, 12, 6, 12, 24, 6, 6, 12, 18, 6, 12, 6, 18, 24, 18, 30, 12, 6, 6, 30, 24, 24, 18, 30, 12, 18, 12, 6, 36, 30, 6, 12, 18, 42, 30, 30, 42, 12, 60, 30, 48, 6, 12, 30, 12, 6, 6, 12, 42, 6, 12, 54, 24, 24, 42, 36, 36, 18, 30, 36, 18, 6, 42, 30, 6, 30, 36, 30, 24, 18, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS a(1) and a(2) are undefined. Alternatively, a(n) = least k, 1 < k < n, such that prime(n) + k and prime(n) - k are both prime. I conjecture that a(n) is defined for all n > 2. Equivalently, every prime > 3 is the average of two distinct primes. a(n) embodies the difference between weak and strong Goldbach conjectures, and therefore between A047160 and A082467 which differ only for prime arguments (a(n)=A082467(prime(n)), while A047160(prime(n))=0). - Stanislav Sykora, Mar 14 2014 LINKS Stanislav Sykora, Table of n, a(n) for n = 3..40000 FORMULA a(n) = A082467(A000040(n)). - Jason Kimberley, Jun 25 2012 EXAMPLE prime(3) = 5 is the center of the interval [3,7] that has prime endpoints; this interval has radius = 7-5 = 2. Hence a(3) = 2. prime(5) = 11 is the center of the interval [5,17] that has prime endpoints; this interval has radius = 17-11 = 6. Hence a(5) = 6. MATHEMATICA f[n_] := Module[{p, k}, p = Prime[n]; k = 1; While[(k < p) && (! PrimeQ[p - k] || ! PrimeQ[p + k]), k = k + 1]; k]; Table[f[i], {i, 3, 103}] PROG (PARI) StrongGoldbachForPrimes(nmax)= {local(v, i, p, k); v=vector(nmax); for (i=1, nmax, p=prime(i); v[i] = -1; for (k=1, p-2, if (isprime(p-k)&&isprime(p+k), v[i]=k; break; ); ); ); return (v); } \\ Stanislav Sykora, Mar 14 2014 CROSSREFS Cf. A047160, A082467. - Stanislav Sykora, Mar 14 2014 Sequence in context: A174342 A111150 A166983 * A211376 A278249 A131450 Adjacent sequences:  A078608 A078609 A078610 * A078612 A078613 A078614 KEYWORD nonn,easy AUTHOR Joseph L. Pe, Dec 09 2002 STATUS approved

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Last modified September 26 02:28 EDT 2020. Contains 337346 sequences. (Running on oeis4.)