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 A351054 First of three consecutive primes p,q,r such that p+q-r, p-q+r, -p+q+r are all prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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: A179730 A287900 A139411 * 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

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Last modified March 24 12:49 EDT 2023. Contains 361479 sequences. (Running on oeis4.)