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 A356475 First of three consecutive primes p,q,r such that p*q + q*r + r*p is prime. 4
 2, 3, 5, 7, 17, 29, 37, 41, 43, 67, 83, 103, 137, 157, 179, 181, 193, 227, 277, 283, 347, 359, 383, 431, 457, 461, 607, 661, 701, 709, 757, 773, 823, 827, 839, 859, 937, 967, 1013, 1051, 1061, 1109, 1129, 1187, 1201, 1213, 1249, 1283, 1307, 1327, 1373, 1423, 1439, 1471, 1481, 1487, 1543, 1567 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(4) = 7 is a term because 7, 11, 13 are three consecutive primes with 7*11 + 11*13 + 13*7 = 311 which is prime. MAPLE R:= NULL: count:= 0: P:= Vector(3, ithprime): while count < 100 do x:= P[1]*P[2]+P[2]*P[3]+P[3]*P[1]; if isprime(x) then R:= R, P[1]; count:= count+1 fi; P[1..2]:= P[2..3]; P[3]:= nextprime(P[3]); od: R; MATHEMATICA Select[Partition[Prime[Range[250]], 3, 1], PrimeQ[Total[# * RotateLeft[#]]] &][[;; , 1]] (* Amiram Eldar, Aug 08 2022 *) PROG (Python) from itertools import islice from sympy import isprime, nextprime def agen(): p, q, r = 2, 3, 5 while True: if isprime(p*q + q*r + r*p): yield p p, q, r = q, r, nextprime(r) print(list(islice(agen(), 58))) # Michael S. Branicky, Aug 08 2022 (PARI) list(lim)=my(v=List(), p=2, q=3); forprime(r=5, nextprime(nextprime(lim\1+1)+1), if(isprime(p*q + q*r + r*p), listput(v, p)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Sep 06 2022 CROSSREFS Cf. A189759, A356471, A356477. Sequence in context: A060212 A107439 A262836 * A178382 A360591 A289757 Adjacent sequences: A356472 A356473 A356474 * A356476 A356477 A356478 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Aug 08 2022 STATUS approved

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