

A240699


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

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


EXAMPLE

Prime number 191: the closest prime number to 191 is 193 with 193191 = 2 <= 6. So 191 is in this sequence.
Prime number 211: the closest prime number to 211 is 199 with 211199=12 > 6. So 211 is not in this sequence.


MATHEMATICA

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


PROG

(PARI) forprime(p=3, 250, if(pprecprime(p1)<7, print1(p, ", "), if(nextprime(p+1)p<7, print1(p, ", ")))) \\ Felix FrÃ¶hlich, Aug 16 2014; corrected by Michel Marcus, May 26 2018


CROSSREFS

Cf. A000040, A167833, A137870.
Sequence in context: A065091 A160656 A176997 * A065380 A211075 A038134
Adjacent sequences: A240696 A240697 A240698 * A240700 A240701 A240702


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Apr 10 2014


STATUS

approved



