A381616 a(n) is the smallest prime that starts the first occurrence of exactly n consecutive primes in A381019.

7643, 31, 3517, 1049, 2, 41, 173, 401, 523, 113, 337, 449, 6599, 251, 1993, 2543, 743, 593, 1481, 1301, 1069, 2357, 17657, 4079, 2797, 8219, 64123, 81299, 19289, 40129, 6709, 13999, 4271, 1669, 37579, 28793, 38039, 12413, 125711, 24907, 3181, 41597, 27253

Offset

1,1

Comments

As the sequence grows, increasingly longer chains of consecutive prime numbers begin to appear.

Conjecture: a(n) always exists.

Links

Table of n, a(n) for n=1..43.

Example

For n = 2, we observe that 9, 31, 37, and 8 are four consecutive terms of A381019, where 31 and 37 are exactly two consecutive primes and represent the first occurrence of two consecutive terms that are prime. So, a(2) = 31.

Crossrefs

Cf. A381019, A381117.

Sequence in context: A252968 A252051 A038011 * A381027 A205040 A252406

Adjacent sequences: A381613 A381614 A381615 * A381617 A381618 A381619

Keyword

nonn

Author

Gonzalo Martínez, Mar 01 2025

Status

approved