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A294064
Numbers k such that 2*k - 3, 2*k + 3, 3*k - 2, 3*k + 2 are primes.
1
5, 7, 13, 35, 43, 55, 77, 127, 133, 155, 167, 253, 287, 295, 365, 475, 497, 533, 595, 713, 1007, 1177, 1483, 1805, 2323, 2575, 2723, 2927, 3107, 3415, 3487, 3823, 4145, 4213, 4367, 4565, 4717, 4927, 4963, 5125, 5215, 5363, 5417, 5587, 5627, 5795, 6133, 6587, 6797
OFFSET
1,1
COMMENTS
The common numbers of A098090, A067076, A153183, A024893.
Conjecture: The Sum_{n>=1} 1/a(n) = 0.57... converges.
Note that the sum of the 4 primes that are obtained is 10 times the original term: (2*k - 3) + (2*k + 3) + (3*k - 2) + (3*k + 2) = 10*k.
From Robert G. Wilson v, Nov 19 2017: (Start)
Number of terms less than 10^m: 2, 7, 20, 55, 189, 919, 4863, 28218, 174469, ..., ;
Number of prime terms less than 10^m: 2, 4, 6, 12, 39, 140, 558, 2755, 14804, ..., .
All terms are == {5, 7, 13, 17, 23, 25} (mod 30).
(End)
LINKS
EXAMPLE
5 is in the sequence because 2*5-3 = 7, 2*5+3 = 13, 3*5-2 = 13, 3*5+2 = 17 and the tetrad [7, 13, 13, 17] are all prime numbers.
7 is in the sequence because 2*7-3 = 11, 2*7+3 = 17, 3*7-2 = 19, 3*7+2 = 23 and the tetrad [11, 17, 19, 23] are all prime numbers.
MATHEMATICA
Select[Range[10^4], Function[k, AllTrue[Flatten@ Map[#1 k + {-1, 1} #2 & @@ # &, {#, Reverse@ #}] &@ {2, 3}, PrimeQ]]] (* Michael De Vlieger, Oct 22 2017 *)
PROG
(PARI) {
for(n=1, 10000,
if(isprime(2*n-3)&&isprime(2*n+3)&&isprime(3*n-2)&&isprime(3*n+2),
print1(n", ")
)
)
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Dimitris Valianatos, Oct 22 2017
STATUS
approved