OFFSET
1,10
LINKS
Benjamin Green and Terence Tao, Linear equations in primes, arXiv:math/0606088 [math.NT], 2006-2008; Annals of Mathematics Second Series, Vol. 171, No. 3 (May, 2010), pp. 1753-1850.
Ben J. Green and Terence C. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), pp. 481-547.
FORMULA
a(n) ~ Cp^2/log^4 p ~ Cn^2/log^2 n where p is the n-th prime and C = A351909.
PROG
(PARI) a(n, qlim=prime(n))=my(s); forprime(q=23, qlim, forprimestep(p=q%6, q-18, 6, isprime((2*p+q)/3) && isprime((2*q+p)/3) && s++)); s
(PARI) b(q)=my(s); forprimestep(p=q%6, q-18, 6, isprime((2*p+q)/3) && isprime((2*q+p)/3) && s++); s
first(n)=my(v=vector(n), s, i); forprime(p=2, prime(n), v[i++]=s+=b(p)); v
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV, Feb 25 2022
STATUS
approved