A137870 -id:A137870 - cp's OEIS frontend

A167833 Three-times-isolated primes: primes p such that neither p+-2, p+-4 nor p+-6 is prime.

2, 211, 293, 409, 479, 631, 691, 701, 709, 719, 787, 797, 839, 919, 929, 1163, 1171, 1201, 1249, 1259, 1381, 1399, 1409, 1471, 1511, 1523, 1531, 1637, 1709, 1733, 1801, 1811, 1823, 1831, 1847, 1889, 2039, 2053, 2099, 2153, 2161, 2179, 2221, 2251, 2459

Offset: 1

Juri-Stepan Gerasimov, Nov 13 2009

nonn

2 together with prime numbers, isolated from neighboring primes by>6.

			a(1)=2 (-4,-2,0,4,6,8 are nonprimes); a(2)=211 (205,207,209,213,215,217 are nonprimes).

Harvey P. Dale, Table of n, a(n) for n = 1..2500

Cf. A137870, A167771.

Join[{2},Select[Prime[Range[400]],NoneTrue[#+{2,4,6,-2,-4,-6},PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 16 2019 *)

A240699 Primes p such that at least one number among p+-2, p+-4, p+-6 is also a prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Lei Zhou, Apr 10 2014

The union of A167833 and this sequence is the set of all prime numbers, A000040.

			Prime number 191: the closest prime number to 191 is 193 with 193-191 = 2 <= 6. So 191 is in this sequence.
Prime number 211: the closest prime number to 211 is 199 with 211-199=12 > 6. So 211 is not in this sequence.

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

Cf. A000040, A167833, A137870.

p = 2; Table[While[p = NextPrime[p]; ((NextPrime[p] - p) > 6) && (6 < (p - NextPrime[p, -1]))]; p, {n, 1, 58}]

forprime(p=3, 250, if(p-precprime(p-1)<7, print1(p, ", "), if(nextprime(p+1)-p<7, print1(p, ", ")))) \\ Felix Fröhlich, Aug 16 2014; corrected by Michel Marcus, May 26 2018

cp's OEIS Frontend

A167833 Three-times-isolated primes: primes p such that neither p+-2, p+-4 nor p+-6 is prime.

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