A342705 Primes p such that (p^2 - p*q + q^2)/3 is prime, where q is the next prime after p.
5, 7, 13, 17, 19, 59, 97, 101, 107, 109, 191, 223, 229, 277, 283, 569, 613, 631, 643, 709, 719, 743, 829, 857, 881, 1031, 1049, 1051, 1091, 1109, 1171, 1193, 1249, 1277, 1301, 1327, 1489, 1579, 1637, 1697, 1949, 1979, 2003, 2081, 2089, 2113, 2141, 2203, 2357, 2423, 2539, 2593, 2659, 2749, 2789, 2819
Offset: 1
Keywords
Examples
a(5) = 19 is a term because 19 and 23 are consecutive primes and (19^2 - 19*23 + 23^2)/3 = 151 is prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
R:= NULL: q:= 2: count:= 0: while count < 100 do p:= q; q:= nextprime(p); r:= (p^2-p*q+q^2)/3; if r::integer and isprime(r) then count:= count+1; R:= R, p; fi; od: R; -
Python
from sympy import isprime, nextprime def aupto(limit): p, q, num, alst = 2, 3, 7, [] while p <= limit: if num%3 == 0 and isprime(num//3): alst.append(p) p, q = q, nextprime(q) num = p**2 - p*q + q**2 return alst print(aupto(2819)) # Michael S. Branicky, Mar 18 2021
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