A338543 Numbers k such that 1 + Product_{i<k} prime(i) is divisible by prime(k).

1, 2, 8, 233, 431

Offset

1,2

Comments

Numbers k such that A062347(k-1) == -1 (mod prime(k)).

Links

Table of n, a(n) for n=1..5.

Mathematics StackExchange, Is 510511 the smallest euclid number e_n that divides by the next prime p.

Formula

a(n) = A081618(n)+1 for n >= 2.

Example

a(3)=8 is a term because 1 + 2*3*5*7*11*13*17 = 510511 is divisible by prime(8)=19.

Maple

select(t -> 1+mul(ithprime(i), i=1..t-1) mod ithprime(t)=0, [$1..1000]);

Prog

(PARI) isok(n) = ((1+vecprod(primes(n-1))) % prime(n)) == 0; \\ Michel Marcus, Nov 03 2020

Crossrefs

Cf. A002110, A006862, A081618, A062347, A341805.

Sequence in context: A013344 A091503 A009588 * A125264 A028985 A067583

Adjacent sequences: A338540 A338541 A338542 * A338544 A338545 A338546

Keyword

nonn,more

Author

Robert Israel, Nov 01 2020

Status

approved