A359939 Lexicographically earliest strictly increasing sequence of primes whose partial products lie between noncomposite numbers.

2, 3, 5, 19, 41, 67, 113, 653, 883, 1439, 3823, 10631, 12841, 14251, 23357, 27103, 30491, 64679, 78823, 110977, 115127, 118747, 159431, 215587, 301039, 342257, 343639, 428401, 473383, 493583, 566723, 621133, 638371, 639157, 680539, 904049, 993037, 1146133, 1252507

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..150

Example

2 - 1 = 1 and 2 + 1 = 3 are both noncomposite numbers.
2*3 - 1 = 5 and 2*3 + 1 = 7 are both noncomposite numbers.
2*3*5 - 1 = 29 and 2*3*5 + 1 = 31 are both noncomposite numbers.

Mathematica

a[1] = 2; a[n_] := a[n] = Module[{r = Product[a[k], {k, 1, n-1}], p = NextPrime[a[n-1]]}, While[!PrimeQ[r*p-1] || !PrimeQ[r*p+1], p = NextPrime[p]]; p]; Array[a, 50]

Crossrefs

Cf. A008578, A014574, A039726, A087898, A167777, A359940.

Sequence in context: A174161 A072532 A215373 * A038705 A066754 A140560

Adjacent sequences: A359936 A359937 A359938 * A359940 A359941 A359942

Keyword

nonn

Author

Amiram Eldar, Jan 19 2023

Status

approved