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A351054
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First of three consecutive primes p,q,r such that p+q-r, p-q+r, -p+q+r are all prime.
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1
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228647, 642457, 3678317, 4424699, 5507669, 8439073, 8527301, 8545387, 9207197, 9490571, 9843049, 10023817, 10148123, 10670909, 11621243, 11697979, 12208459, 12409849, 12687119, 12845879, 12947071, 13590457, 13940057, 14377747, 14511053, 15309937, 16628009, 16713731, 16982153, 17073041, 17302639
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OFFSET
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1,1
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COMMENTS
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Each term is the second in an arithmetic progression of five primes, of which at least the second, third and fourth are consecutive primes.
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..1000
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EXAMPLE
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a(3) = 3678317 is a term because it is prime, the next two primes are 3678347 and 3678377, and 3678317+3678347-3678377 = 3678287, 3678317-3678347+3678377 = 3678347, and -3678317+3678347+3678377 = 3678407 are all primes.
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MAPLE
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f:= proc(p, q, r)
isprime(p+q-r) and isprime(p-q+r) and isprime(-p+q+r)
end proc:
p:= 2: q:= 3: r:= 5: R:= NULL: count:= 0:
while r < 10^8 do
p:= q; q:= r; r:= nextprime(r);
if f(p, q, r) then count:= count+1; R:= R, p fi
od:
R;
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PROG
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(Python)
from sympy import isprime, nextprime
def c(p, q, r): return isprime(p+q-r) and isprime(p-q+r) and isprime(-p+q+r)
def afind():
p, q, r = 2, 3, 5
while True:
if c(p, q, r): print(p, end=", ")
p, q, r = q, r, nextprime(r)
afind() # Michael S. Branicky, Jan 30 2022
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CROSSREFS
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Sequence in context: A179730 A287900 A139411 * A212727 A234670 A324636
Adjacent sequences: A351051 A351052 A351053 * A351055 A351056 A351057
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot and Robert Israel, Jan 30 2022
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STATUS
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approved
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