A080373 a(n) is the smallest number k such that GCD of n values of prime(j)-1 for successive j values starting with k is greater than 2, where prime(j) = j-th prime.

3, 6, 24, 77, 271, 271, 1395, 1395, 1395, 13717, 34369, 172146, 172146, 804584, 804584, 804584, 12762142, 16138563, 16138563, 56307979, 56307979, 56307979, 56307979, 56307979, 1857276773, 3511121443

Offset: 1

Author

Labos Elemer, Feb 26 2003

Keywords

• nonn
• more

Examples

			For n = 2: a(2) = 6 = A067605(2).
For n = 3: a(3) = 24 means: firstly occurs that for three consecutive p-1 terms GCD[prime(24)-1, prime(25)-1, prime(26)-1] = GCD[88, 96, 100] = 4 > 2;
		

Crossrefs

Cf. A058263, A067605.

Programs

PARI

a(n) = {my(k = 0, v = vector(n, i, prime(i)-1)); if(gcd(v) > 2, return(0)); forprime(p = v[n]+1, , k++; v = concat(vecextract(v, "^1"), p-1); if(gcd(v) > 2, return(k)));} \\ Amiram Eldar, Jun 22 2024

Formula

a(n) = Min{x; gcd[prime(x)-1, ..., prime(x+n-1)] > 2}, where prime() = A000040().

Extensions

a(1) corrected and a(17)-a(26) added by Amiram Eldar, Jun 22 2024