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A086715
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Primes p such that A001414(p-1) and A001414(p+1) are both prime, where A001414 = sum of primes dividing n (with repetition).
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1
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11, 53, 89, 251, 359, 383, 389, 463, 487, 809, 857, 863, 1109, 1217, 1429, 1451, 1549, 2039, 2089, 2459, 2903, 3037, 3457, 3541, 3709, 3727, 3739, 4259, 4373, 4451, 4733, 4903, 5641, 5851, 5939, 6359, 7019, 7079, 7129, 7219, 7549, 8059, 8839, 8929, 9007
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(2)=53 because it is prime and 52=2^2*13, 54=2*3^3 and 2+2+13=17 and 2+3+3+3=11.
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MATHEMATICA
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primeSopfQ[n_] := PrimeQ[Plus @@ Times @@@ FactorInteger[n]]; seqQ[n_] := PrimeQ[n] && AllTrue[{n - 1, n + 1}, primeSopfQ]; Select[Range[10^4], seqQ] (* Amiram Eldar, Dec 14 2019 *)
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PROG
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(Magma) [ n : n in [3..9100] | IsPrime(n) and IsPrime(&+[ k[1]*k[2] : k in Factorization(n-1)]) and IsPrime(&+[ k[1]*k[2] : k in Factorization(n+1)]) ]; /* Klaus Brockhaus, Mar 24 2007 */
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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