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URL: https://oeis.org/A389823

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A389823
Indices k such that the product of the first k prime gaps plus 1 is prime.
1
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
OFFSET
1,2
COMMENTS
a(37) > 20000. - Michael S. Branicky, Dec 27 2025
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
Sequence in context: A056513 A056518 A160644 * A347734 A267459 A330357
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