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 A339698 Primes of the form p^2 - p*q + q^2, where p and q are consecutive primes. 3
 7, 19, 3163, 23743, 28927, 70783, 141403, 198943, 223837, 265333, 283267, 329503, 1136383, 1223263, 1254427, 1488427, 2238043, 2421163, 3625243, 3904603, 4709143, 4884127, 5216683, 5784133, 7376683, 8065627, 8797183, 10660333, 11242717, 12348223, 16613803, 18594019, 19202167, 19999027 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 (first 100 terms from Zak Seidov) EXAMPLE a(2) = 19 = 3^2 - 3*5 + 5^2 is the only prime obtained with a pair of twin primes: (3, 5). - Bernard Schott, Dec 23 2020 MATHEMATICA Select[Map[#1^2 - #1 #2 + #2^2 & @@ # &, Partition[Prime@ Range[610], 2, 1]], PrimeQ] (* Michael De Vlieger, Dec 13 2020 *) PROG (PARI) forprime(p=1, 1e4, my(q=nextprime(p+1), x=p^2-p*q+q^2); if(ispseudoprime(x), print1(x, ", "))) \\ Felix Fröhlich, Dec 14 2020 (PARI) first(n) = { my(q = 2, p, res = vector(n), t = 0); forprime(p = 3, oo, c = p^2 - p*q + q^2; if(isprime(c), t++; res[t] = c; if(t >= n, return(res) ) ); q = p; ) } \\ David A. Corneth, Dec 19 2020 CROSSREFS Cf. A243761 (similar, with p^2 + p*q + q^2), A339920 (the primes p). Sequence in context: A057866 A329001 A334982 * A301808 A128817 A284897 Adjacent sequences: A339695 A339696 A339697 * A339699 A339700 A339701 KEYWORD nonn AUTHOR Zak Seidov, Dec 13 2020 STATUS approved

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Last modified August 13 11:30 EDT 2024. Contains 375131 sequences. (Running on oeis4.)