A363017 a(n) is the least integer k such that the k-th, (k+1)-th, ..., (k+n-1)-th primes are congruent to 3 mod 8.

2, 94, 334, 4422, 23969, 303493, 303493, 606529, 28725046, 92865581, 397316305, 511883558, 848516256, 23738949809, 144899085865, 469694200388, 3800553021301, 8571139291304, 63858322306341, 90990757864814

Offset: 1

Author

Léo Gratien, May 13 2023

Keywords

• nonn
• more

Comments

a(n) is also the minimal rank where n consecutive 2's appear in A023512.

The sequence is infinite by Shiu's theorem.

Examples

			For n=2, a(2) = 94 because prime(94)+1 = 492 = 4*123, prime(95)+1 = 500 = 4*125 are the first two consecutive primes p such that p+1 is divisible by 4 and not by 8.
		

Crossrefs

Cf. A057632, A023512.

Cf. A363016 (with 1 mod 4).

Formula

a(n) = primepi(A057632(n)). - Amiram Eldar, May 13 2023

Extensions

a(19)-a(20) from Martin Ehrenstein, May 28 2023