A083565 Begins the first chain of n consecutive primes whose product - 2 is prime.

5, 3, 3, 3, 3, 3, 3, 3, 23, 3, 131, 3, 67, 7, 3, 43, 461, 523, 3, 1021, 113, 3877, 5, 19, 1493, 3, 5, 7, 3187, 5, 593, 2633, 5, 661, 3371, 179, 3889, 3, 839, 443, 3023, 1579, 1613, 251, 139, 751, 3343, 229, 5233, 4153

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

3 is the smallest prime in 3, 5, 7, 11 which is the first chain of four consecutive primes whose product - 2 is prime: 3 * 5 * 7 * 11 - 2 = 1153 (prime). Hence a(4) = 3.

Prog

(PARI) pchain(p, n) = {my(pp = p, i, q); for (i=1, n-1, q = nextprime(p+1); pp *= q; p = q; ); return (pp-2); }
lista(nn) = {for (n = 1, nn, p = 3; while (! isprime(pchain(p, n)), p = nextprime(p+1); ); print1(p, ", "); ); } \\ Michel Marcus, May 18 2013

Crossrefs

Sequence in context: A057435 A246728 A155685 * A359199 A212493 A011320

Adjacent sequences: A083562 A083563 A083564 * A083566 A083567 A083568

Keyword

nonn

Author

Joseph L. Pe, Jun 12 2003

Extensions

More terms from Michel Marcus, May 18 2013

a(1)=5 prepended by Sean A. Irvine, Feb 05 2026

Status

approved