A167706 - OEIS

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.

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

Equals 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

(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

CROSSREFS

Cf. A007510, A014574.

Sequence in context: A332640 A296505 A325283 * A331091 A072121 A349179

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