|
|
A248085
|
|
Initial prime of 4 primes in arithmetic progression with difference 12.
|
|
2
|
|
|
5, 7, 17, 47, 127, 227, 257, 397, 467, 607, 997, 1447, 1487, 1697, 1877, 2647, 3307, 3547, 3907, 4217, 4987, 5407, 6287, 6947, 7297, 7537, 7817, 10067, 10627, 11047, 11777, 12227, 12577, 13147, 14747, 15137, 15737, 15877, 17827, 19727, 19937, 20707, 21577, 22027, 22247, 23017, 24097, 26017
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Or, primes p such that p + 12, p + 24 and p + 36 are also primes.
Primes are not necessarily consecutive ones. A033447 is subsequence: a(92) = 111497 = A033447(1), a(144) = 258527 = A033447(2), etc.
The only case with p + 48 prime is p = 5, in all other cases p + 48 is divisible by 5.
All terms >5 are congruent to 7 (mod 10). - Zak Seidov, Jun 12 2018
|
|
LINKS
|
|
|
MAPLE
|
A248085:=n->`if`(isprime(n) and isprime(n+12) and isprime(n+24) and isprime(n+36), n, NULL): seq(A248085(n), n=1..10^5); # Wesley Ivan Hurt, Oct 01 2014
|
|
MATHEMATICA
|
Select[Prime[Range[1000]], PrimeQ[# + 12] && PrimeQ[# + 24] && PrimeQ[# + 36] &] (* Alonso del Arte, Oct 01 2014 *)
Select[Prime[Range[3000]], AllTrue[#+{12, 24, 36}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 08 2016 *)
|
|
PROG
|
(PARI) forprime(p=5, 10^5, isprime(p+12)&&isprime(p+24)&&isprime(p+36)&&print1(p", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|