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A272367
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Primes p separated from their adjacent primes on both sides by a prime number of successive composites, while the adjacent primes of p are separated by a prime number of integers.
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1
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53, 89, 97, 113, 127, 157, 173, 211, 257, 263, 307, 317, 331, 359, 367, 373, 389, 397, 401, 449, 457, 479, 487, 491, 499, 509, 541, 563, 593, 607, 653, 683, 727, 733, 743, 751, 761, 769, 773, 853, 863, 877, 887, 907, 911, 937, 947, 953, 967, 977, 983, 991, 997, 1069, 1103, 1109, 1117, 1123, 1187
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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(1) = 53. The primes around and including 53 are {47, 53, 59}. The number of composites between these are {5, 5} and the number of integers between 47 and 59 is 11; all of {5, 5, 11} are prime, thus 53 is a term.
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MATHEMATICA
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Select[Prime@ Range@ 195, Function[p, Times @@ Boole@ PrimeQ@ Flatten[Map[Differences, {#, Delete[#, 2]}] - 1] &@ Map[NextPrime[p, #] &, Range[-1, 1]] == 1]] (* Michael De Vlieger, Apr 27 2016 *)
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PROG
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(PARI) list(lim)=my(v=List(), p=2, q=3); forprime(r=5, nextprime(lim\1+1), if(isprime(q-p-1) && isprime(r-q-1) && isprime(r-p-1), listput(v, q)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Apr 30 2016
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CROSSREFS
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KEYWORD
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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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