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A167706
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The single or isolated numbers. The union of single (or isolated or non-twin) primes and single (or isolated or average of twin prime pairs) nonprimes.
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21
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2, 4, 6, 12, 18, 23, 30, 37, 42, 47, 53, 60, 67, 72, 79, 83, 89, 97, 102, 108, 113, 127, 131, 138, 150, 157, 163, 167, 173, 180, 192, 198, 211, 223, 228, 233, 240, 251, 257, 263, 270, 277, 282, 293, 307, 312, 317, 331, 337, 348, 353, 359, 367, 373, 379, 383, 389
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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MATHEMATICA
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With[{nn = 78}, {2}~Join~Union[Transpose[Select[Partition[Prime@ Range@ nn, 3, 1], And[#[[2]] - #[[1]] != 2, #[[3]] - #[[2]] != 2] &]][[2]], Map[Mean, Select[Partition[Prime@ Range@ nn, 2, 1], Differences@ # == {2} &]]]] (* Michael De Vlieger, Feb 22 2017, after Harvey P. Dale at A007510 and A014574 *)
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PROG
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(PARI) is(n)=if(n%6, (isprime(n) && !isprime(n-2) && !isprime(n+2)) || n==4, isprime(n-1) && isprime(n+1)) \\ Charles R Greathouse IV, Apr 29 2015
(PARI) lista(pmax) = {my(p1 = 2, p2 = 3); print1(2, ", "); forprime(p3 = 5, pmax, if(p2 == p1 + 2, print1(p1 + 1, ", ")); if(p2 != p1 + 2 && p2 != p3 - 2, print1(p2, ", ")); p1 = p2; p2 = p3); } \\ Amiram Eldar, May 17 2024
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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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