A098142 - OEIS

A098142

Numbers n such that (p*(q-1)+(p-1)*q)/2 is prime, where p and q are consecutive odd primes, p<q and p_n is the n-th prime.

%I #9 Feb 23 2023 16:39:26

%S 2,3,5,9,13,15,17,26,35,43,56,60,80,81,83,86,89,101,102,104,120,140,

%T 152,157,170,178,191,201,204,215,219,223,238,252,286,293,296,324,329,

%U 350,359,373,383,392,395,398,412,416,424,444,458,468,479,487,497,503,514

%N Numbers n such that (p*(q-1)+(p-1)*q)/2 is prime, where p and q are consecutive odd primes, p<q and p_n is the n-th prime.

%H Harvey P. Dale, <a href="/A098142/b098142.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, r = (p*(q - 1) + (p - 1)*q)/2; If[ PrimeQ[r], r, 0]]; Select[ Range[522], f[ # ] != 0 &]

%t Position[Partition[Prime[Range[600]],2,1],_?(PrimeQ[(#[[1]](#[[2]]-1)+(#[[1]]-1) #[[2]])/2]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Feb 23 2023 *)

%Y The generator of A099911.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_ and _Robert G. Wilson v_, Nov 02 2004