A389823 - OEIS

A389823

Indices k such that the product of the first k prime gaps plus 1 is prime.

1, 2, 3, 4, 7, 10, 15, 17, 19, 35, 57, 59, 121, 142, 204, 296, 307, 400, 410, 480, 573, 591, 730, 904, 1212, 1436, 1710, 2178, 2307, 2390, 4949, 5949, 6952, 10488, 11977, 12171, 33905, 34143

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OFFSET

1,2

COMMENTS

a(37) > 20000. - Michael S. Branicky, Dec 27 2025

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

Prime gaps start 1, 2, 2, 4, 2, 4, 2, ...

The cumulative products are 1, 2, 4, 16, 32, 128, 256, ...

Adding 1 gives 2, 3, 5, 17, 33, 129, 257, ...

Primes occur at indices 1, 2, 3, 4, 7, ...

MATHEMATICA

seq[max_] := Position[1 + FoldList[Times, Differences[Prime[Range[max]]]], _?PrimeQ] // Flatten; seq[2500] (* Amiram Eldar, Nov 20 2025 *)

CROSSREFS

Cf. A001223, A081411.

Sequence in context: A056513 A056518 A160644 * A347734 A267459 A330357

Adjacent sequences: A389820 A389821 A389822 * A389824 A389825 A389826

KEYWORD

nonn,hard,more

AUTHOR

Arvizzigno Gianni, Nov 18 2025

EXTENSIONS

a(21)-a(30) from Michel Marcus, Nov 20 2025

a(31)-a(33) from Amiram Eldar, Nov 20 2025

a(34)-a(36) from Michael S. Branicky, Dec 27 2025

a(37)-a(38) from Michael S. Branicky, Jan 10 2026

STATUS

approved