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

Author

Gonzalo Martínez, Mar 01 2025

Keywords

• nonn

Comments

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

Conjecture: a(n) always exists.

Examples

			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.