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 A167706 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. 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A167706 = A007510 U A014574. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 FORMULA a(n) ~ n log n. - Charles R Greathouse IV, Apr 29 2015 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A007510, A014574. Sequence in context: A023995 A018189 A239954 * A072121 A175305 A171923 Adjacent sequences:  A167703 A167704 A167705 * A167707 A167708 A167709 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Nov 10 2009, Nov 14 2009 EXTENSIONS Corrected (97 inserted) by R. J. Mathar, Nov 16 2009 STATUS approved

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