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A355804
First of 6 consecutive primes p1,p2,p3,p4,p5,p6 such that (p2-p1)*(p5+p6)+(p3-p2)*(p4+p5)-1 and (p2-p1)*(p5+p6)+(p3-p2)*(p4+p5)+1 are primes.
1
2, 3, 5, 7, 23, 73, 97, 277, 617, 653, 683, 811, 839, 877, 1097, 2029, 2549, 3037, 3067, 3329, 3499, 3659, 3769, 3929, 4127, 4283, 4423, 4447, 4483, 4673, 4871, 5023, 5197, 5261, 5351, 5503, 5623, 5701, 6143, 6323, 6703, 6803, 6823, 7109, 7151, 7187, 7433, 7583, 7907, 8849, 8861, 9203, 9403, 9419
OFFSET
1,1
COMMENTS
First of 6 consecutive primes p1,p2,p3,p4,p5,p6 such that (p2-p1)*(p5+p6)+(p3-p2)*(p4+p5) is in A014574.
LINKS
EXAMPLE
a(3) = 5 is a term because 5, 7, 11, 13, 17, 19 are consecutive primes with (7-5)*(17+19)+(11-7)*(13+17)-1 = 191 and (7-5)*(17+19)+(11-7)*(13+17)+1 = 193 prime.
MAPLE
p2:= 2: p3:= 3: p4:= 5: p5:= 7: p6:= 11:
count:= 0: R:= NULL:
while count < 100 do
p1:= p2: p2:= p3: p3:= p4: p4:= p5: p5:= p6: p6:= nextprime(p6):
t:= (p2-p1)*(p5+p6)+(p3-p2)*(p4+p5);
if isprime(t-1) and isprime(t+1) then
count:= count+1; R:= R, p1;
fi;
od:
R;
MATHEMATICA
scpQ[{a_, b_, c_, d_, e_, f_}]:=AllTrue[(b-a)(e+f)+(c-b)(d+e)+{1, -1}, PrimeQ]; Select[Partition[ Prime[ Range[1200]], 6, 1], scpQ][[;; , 1]] (* Harvey P. Dale, Jun 07 2023 *)
CROSSREFS
Cf. A014574.
Sequence in context: A006510 A006055 A052017 * A277575 A289754 A062088
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 17 2022
STATUS
approved