OFFSET
1,1
COMMENTS
Is the sequence infinite?
Any further terms are > 10^13. - Lucas A. Brown, Sep 23 2024
LINKS
Lucas A. Brown, Python program.
A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.
A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
FORMULA
a(n) = (smallest p(m) = 1 mod 6) such that all 2*n primes p(m-n..m-1) and p(m+1..m+n) = 5 mod 6.
EXAMPLE
a(n) = 7 is sandwiched by primes 5 and 11 (both primes = 5 mod 6),
a(2) = 241 is sandwiched by 2 lesser primes 233, 239 and 2 larger primes 251, 257 (all four primes = 5 mod 6),
a(3) = 967 is sandwiched by 3 lesser primes 941, 947, 953 and 3 larger primes 971, 977, 983 (all six primes = 5 mod 6),
a(4) = 15787 is sandwiched by 4 lesser primes 15749, 15761, 15767, 15773 and 4 larger primes 15791, 15797, 15803, 15809 (all 8 primes = 5 mod 6),
a(5) = 111577 is sandwiched by 5 lesser primes 111497, 111509, 111521, 111533, 111539 and 5 larger primes 111581, 111593, 111599, 111611, 111623 (all 10 primes = 5 mod 6), etc.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Zak Seidov, Mar 19 2012
EXTENSIONS
a(11)-a(15) from Lucas A. Brown, Sep 23 2024
STATUS
approved