A240709 Primes p such that no number among p+-6 and p+-12 is also a prime.

2, 3, 523, 617, 691, 701, 709, 719, 743, 787, 911, 937, 967, 1153, 1171, 1259, 1381, 1399, 1409, 1637, 1667, 1723, 1787, 1831, 1847, 1931, 1933, 1949, 1951, 2053, 2113, 2161, 2179, 2203, 2221, 2311, 2437, 2477, 2503, 2521, 2593, 2617, 2749, 2767, 2819, 2833

Offset

1,1

Comments

The union of A240709 and A240710 is the set of all prime numbers, i.e., A000040.

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Example

For 2, 2+-6 and 2+-12 are all even numbers and composite. So 2 is included.
For 3, 3+-6 and 3+-12 are all multiples of 3. So 3 is included.
For each prime number p between 5 and 521, at least one number among p+-6 and p+-12 is a prime number, thus p is excluded.
For 523, 523 - 12 = 511 = 7*73, 523 - 6 = 517 = 11*47, 523 + 6 = 529 = 23^2, 523 + 12 = 535 = 5*107. They are all composites. So 523 is included.

Mathematica

p = 1; Table[While[p = NextPrime[p]; ok = 0; a1 = p - 12; a2 = p - 6; a3 = p + 6; a4 = p + 12; If[a1 > 0, If[PrimeQ[a1], ok = 1]]; If[a2 > 0, If[PrimeQ[a2], ok = 1]]; If[PrimeQ[a3], ok = 1]; If[PrimeQ[a4], ok = 1]; ok != 0]; p, {n, 1, 46}]

Crossrefs

Cf. A000040, A240710.

Sequence in context: A090510 A348360 A004887 * A264577 A165770 A226148

Adjacent sequences: A240706 A240707 A240708 * A240710 A240711 A240712

Keyword

nonn,easy

Author

Lei Zhou, Apr 10 2014

Status

approved