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

1,1

Comments

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

The sequence is infinite by Shiu's theorem.

Links

Table of n, a(n) for n=1..20.

Formula

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

Example

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).

Sequence in context: A248627 A290936 A287611 * A158980 A343457 A220970

Adjacent sequences: A363014 A363015 A363016 * A363018 A363019 A363020

Keyword

nonn,more

Author

Léo Gratien, May 13 2023

Extensions

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

Status

approved