A058079 - OEIS

%I #14 Feb 26 2023 14:42:23

%S 5,7,19,23,43,73,79,107,149,151,167,173,197,199,211,271,293,313,349,

%T 367,389,409,433,439,457,467,503,509,593,619,643,647,683,773,821,823,

%U 827,863,883,887,997,1019,1051,1069,1217,1223

%N a(n) = p3, where {p1,p2,p3} are 3 consecutive primes with increasing order such that gcd(C(p3,p2), C(p2,p1)) = 1, where C is the binomial coefficient.

%H Charles R Greathouse IV, <a href="/A058079/b058079.txt">Table of n, a(n) for n = 1..10000</a>

%e 73 is here because C(73,71) = 2628 = 4*9*73 and C(71,67) = 971635 = 71*23*17*7*5 are relatively prime.

%t Select[Partition[Prime[Range[200]],3,1],GCD[Binomial[#[[3]],#[[2]]],Binomial[#[[2]], #[[1]]]]==1&][[;;,3]] (* _Harvey P. Dale_, Feb 26 2023 *)

%o (PARI) is(n)=my(p=precprime(n-1),q=precprime(p-1)); gcd(binomial(n,p),binomial(p,q))==1 && isprime(n) && n>4 \\ _Charles R Greathouse IV_, Nov 13 2015

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 13 2000

%E Name corrected by _Charles R Greathouse IV_, Nov 13 2015