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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.
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%I #14 Jun 22 2024 04:04:29

%S 3,6,24,77,271,271,1395,1395,1395,13717,34369,172146,172146,804584,

%T 804584,804584,12762142,16138563,16138563,56307979,56307979,56307979,

%U 56307979,56307979,1857276773,3511121443

%N 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.

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

%e For n = 2: a(2) = 6 = A067605(2).

%e 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;

%o (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

%Y Cf. A058263, A067605.

%K nonn,more

%O 1,1

%A _Labos Elemer_, Feb 26 2003

%E a(1) corrected and a(17)-a(26) added by _Amiram Eldar_, Jun 22 2024