|
|
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.
|
|
0
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Min{x; gcd[prime(x)-1, ..., prime(x+n-1)] > 2}, where prime() = A000040().
|
|
EXAMPLE
|
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;
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(1) corrected and a(17)-a(26) added by Amiram Eldar, Jun 22 2024
|
|
STATUS
|
approved
|
|
|
|