A363016 a(n) is the least integer k such that the k-th, (k+1)-th, ..., (k+n-1)-th primes are congruent to 1 mod 4.

3, 6, 24, 77, 378, 1395, 1395, 1395, 1395, 31798, 61457, 240748, 800583, 804584, 804584, 804584, 16118548, 16138563, 16138563, 56307979, 56307979, 56307979, 56307979, 56307979, 3511121443, 3511121443, 26284355567, 26284355567, 26284355567, 118027458557, 118027458557, 118027458557, 118027458557

Offset

1,1

Comments

a(n) is also the minimal rank where n consecutive 1's appear in A023512.

The sequence is infinite by Shiu's theorem.

Links

Table of n, a(n) for n=1..33.

D. K. L. Shiu, Strings of Congruent Primes, J. Lond. Math. Soc. 61 (2) (2000) 359-373.

Formula

a(n) = A000720(A057624(n)). - Amiram Eldar, May 13 2023

Example

For n=3, a(3) = 24 because prime(24)+1=90, prime(25)+1=98, and prime(26)+1=102 are the first 3 consecutive primes p such that p+1 is divisible by 2 and not by 4.

Crossrefs

Cf. A000720, A057624, A023512.

Cf. A363017 (3 mod 8).

Sequence in context: A054718 A132390 A080373 * A327643 A296215 A152761

Adjacent sequences: A363013 A363014 A363015 * A363017 A363018 A363019

Keyword

nonn

Author

Léo Gratien, May 13 2023

Status

approved