A389714 Numbers k such that the product of the first k prime gaps minus 1 is prime.

3, 5, 6, 9, 11, 12, 17, 19, 23, 38, 39, 49, 56, 82, 138, 167, 199, 365, 419, 607, 670, 1421, 1449, 1957, 2196, 2489, 6276, 7331, 10813, 20554, 33242

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Example

Prime gaps start 1, 2, 2, 4, 2, 4, 2, ...
The cumulative products are 1, 2, 4, 16, 32, 128, 256, ...
Subtracting 1 gives 0, 1, 3, 15, 31, 127, 255, ...
Primes occur at indices 3, 5, 6, 9, 11, 12, 17, ...

Mathematica

seq[lim_] := Position[FoldList[Times, Differences[Prime[Range[lim]]]], _?(PrimeQ[# - 1] &)] // Flatten; seq[1000] (* Amiram Eldar, Jan 09 2026 *)

Crossrefs

Cf. A001223, A081411.

Sequence in context: A367499 A324701 A047271 * A047445 A341349 A248638

Adjacent sequences: A389711 A389712 A389713 * A389715 A389716 A389717

Keyword

nonn,hard,more

Author

Arvizzigno Gianni, Jan 08 2026

Extensions

a(22)-a(29) from Amiram Eldar, Jan 09 2026

a(30)-a(31) from Michael S. Branicky, Jan 10 2026

Status

approved