|
|
A230223
|
|
Primes p such that 3*p-4, 3*p-10, and 3*p-14 are all prime.
|
|
13
|
|
|
7, 11, 17, 19, 31, 37, 47, 59, 79, 107, 131, 151, 157, 229, 317, 367, 409, 431, 479, 499, 521, 541, 739, 787, 1031, 1181, 1307, 1381, 1487, 1601, 1697, 1747, 1951, 2551, 2749, 2767, 2917, 3251, 3391, 3449, 3581, 3931, 4217, 4349, 4447, 4567, 4639, 4721, 4909, 4967
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Conjecture: Any even number greater than 35 can be written as a sum of four terms of this sequence.
Primes in the sequence should be sparser than twin primes although this has not been proved.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 7 since 3*7-4 = 17, 3*7-10 = 11 and 3*7-14 = 7 are prime.
|
|
MATHEMATICA
|
RQ[n_]:=n>5&&PrimeQ[3n-4]&&PrimeQ[3n-10]&&PrimeQ[3n-14]
m=0
Do[If[RQ[Prime[n]], m=m+1; Print[m, " ", Prime[n]]], {n, 1, 1000}]
Select[Prime[Range[700]], AllTrue[3#-{4, 10, 14}, PrimeQ]&] (* Harvey P. Dale, Sep 29 2023 *)
|
|
PROG
|
(PARI) is(p)=isprime(p) && isprime(3*p-4) && isprime(3*p-10) && isprime(3*p-14) \\ Charles R Greathouse IV, Oct 12 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|