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A341802 Primes p such that (q*s-p*r)/2 and |p*s-q*r|/2 are both prime, where p,q,r,s are consecutive primes. 1
313, 773, 1451, 1733, 2417, 2531, 3041, 3673, 7187, 7297, 7309, 7349, 9479, 9649, 10247, 10631, 11003, 11941, 12197, 12739, 13163, 14449, 16427, 16811, 19801, 21089, 22639, 24029, 24781, 26141, 26237, 26713, 29399, 30097, 30161, 30869, 31051, 33083, 33931, 34667, 37907, 40519, 40543, 40973, 41387 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Intersection of A342505 with union of A342508 and A342509.
LINKS
EXAMPLE
a(3) = 1451 is a term because 1451, 1453, 1459, 1471 are consecutive primes with (1453*1471-1451*1459)/2 = 10177 and |1451*1471-1453*1459|/2 = 7247 both prime.
MAPLE
R:= NULL: count:= 0:
q:= 3: r:= 5: s:= 7:
while count < 100 do
p:= q; q:= r; r:= s; s:= nextprime(s);
if isprime(abs(p*s-q*r)/2) and isprime((q*s-p*r)/2) then
count:= count+1; R:= R, p;
fi
od:
R:
MATHEMATICA
Select[Partition[Prime[Range[4500]], 4, 1], AllTrue[{(#[[2]]#[[4]]-#[[1]]#[[3]])/2, (#[[1]]#[[4]]- #[[2]] #[[3]])/2}, PrimeQ]&][[;; , 1]] (* Harvey P. Dale, Dec 24 2023 *)
CROSSREFS
Sequence in context: A087364 A090514 A068681 * A082436 A108845 A348170
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Mar 14 2021
STATUS
approved

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Last modified July 20 18:43 EDT 2024. Contains 374459 sequences. (Running on oeis4.)