A339698 Primes of the form p^2 - p*q + q^2, where p and q are consecutive primes.

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

Offset: 1

Author

Zak Seidov, Dec 13 2020

Keywords

• nonn

Examples

			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
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 100 terms from Zak Seidov)

Crossrefs

Cf. A243761 (similar, with p^2 + p*q + q^2), A339920 (the primes p).

Programs

Mathematica

Select[Map[#1^2 - #1 #2 + #2^2 & @@ # &, Partition[Prime@ Range[610], 2, 1]], PrimeQ] (* Michael De Vlieger, Dec 13 2020 *)

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