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Numbers k such that (product of first k primes)-1 is divisible by the (k+1)-th prime.
4

%I #11 Mar 03 2021 22:05:06

%S 0,2,4,9823712

%N Numbers k such that (product of first k primes)-1 is divisible by the (k+1)-th prime.

%F a(n) = A000720(A341804(n)) - 1.

%e 4 is a member because 2*3*5*7-1 (product of first 4 primes, minus one) is divisible by the 5th prime, 11.

%e 9823712 is a member because 2*3*5*...*176078267-1 is divisible by 176078293, where 176078267 is the 9823712th prime.

%o (PARI) isok(k) = ((vecprod(primes(k)) - 1) % prime(k+1)) == 0; \\ _Michel Marcus_, Mar 03 2021

%Y Cf. A079276, A081618, A338543, A341804, A341812.

%K nonn,hard,more

%O 1,2

%A _Jeppe Stig Nielsen_, Feb 20 2021