A210248 Smallest prime = 1 mod 6 sandwiched by n smaller and n larger primes = 5 mod 6.

7, 241, 967, 15787, 111577, 1587499, 25230061, 118194961, 188698981, 761453863, 855198067, 855198067, 131320994401, 473676340087, 8775105756643

Offset: 1

Author

Zak Seidov, Mar 19 2012

Keywords

• nonn
• more
• hard

Comments

Is the sequence infinite?

Any further terms are > 10^13. - Lucas A. Brown, Sep 23 2024

Examples

			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.
		

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.

Extensions

a(11)-a(15) from Lucas A. Brown, Sep 23 2024