A387387 Least prime p such that p, p+x_1, ..., p+x_1+...+x_k are consecutive primes, where (x_1, ..., x_k) is the n-th composition corresponding to an admissible prime tuple pattern (see A387383); i.e., first column of A387386.

2, 3, 7, 23, 7, 5, 89, 23, 29, 5, 139, 31, 19, 7, 199, 139, 89, 47, 31, 1601, 397, 19, 67, 7, 137, 29, 17, 5, 113, 509, 359, 89, 83, 47, 23, 197, 137, 149, 29, 1997, 17, 1831, 211, 241, 181, 331, 151, 73, 31, 463, 487, 43, 1597, 277, 67, 13, 7, 523, 1933, 113, 1531

Offset

1,1

Comments

The first Hardy-Littlewood conjecture (or the k-tuple conjecture) implies that such a prime exists for all n; otherwise a(n) = 0.

Links

Table of n, a(n) for n=1..61.

Wikipedia, First Hardy-Littlewood conjecture.

Wikipedia, Prime k-tuple.

Example

For n = 8: A387383(8) = 130, the 130th composition in graded reverse lexicographic order ("standard order", see A066099) is (6,2), the smallest prime p such that p, p+6, and p+6+2 = p+8 are consecutive primes is p = 23 = a(8) (the first term of A049438).

Crossrefs

First column of A387386.

Cf. A049438, A066099, A387383, A387385 (not necessarily consecutive primes).

Sequence in context: A072214 A233535 A007660 * A158055 A156615 A158054

Adjacent sequences: A387384 A387385 A387386 * A387388 A387389 A387390

Keyword

nonn

Author

Pontus von Brömssen, Aug 29 2025

Status

approved