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

Author

Amiram Eldar, Jan 19 2023

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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]