A351054 First of three consecutive primes p,q,r such that p+q-r, p-q+r, -p+q+r are all prime.

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

Offset

1,1

Comments

Each term is the second in an arithmetic progression of five primes, of which at least the second, third and fourth are consecutive primes.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

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.

Maple

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;

Prog

(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

Crossrefs

Sequence in context: A139411 A365891 A365885 * A212727 A234670 A324636

Adjacent sequences: A351051 A351052 A351053 * A351055 A351056 A351057

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 30 2022

Status

approved