A153376 - OEIS

A153376

Smaller of two consecutive prime numbers such that p1*p2*d + d = average of twin prime pairs, d (delta) = p2 - p1.

%I #12 Oct 04 2021 08:39:19

%S 5,7,41,43,101,103,113,227,331,379,569,647,733,751,863,971,1093,1123,

%T 1163,1217,1381,1499,2063,2131,2179,2311,2357,2399,2707,2711,3709,

%U 4789,4817,5021,5051,5171,5479,5501,5987,6011,6827,6949,6967,7103,7213,7477

%N Smaller of two consecutive prime numbers such that p1*p2*d + d = average of twin prime pairs, d (delta) = p2 - p1.

%C See A153377 for the corresponding larger prime.

%H Amiram Eldar, <a href="/A153376/b153376.txt">Table of n, a(n) for n = 1..10000</a>

%e 5*7*2 + 2 = 72 and 72 +- 1 are primes, so 5 is a term.

%e 7*11*4 + 4 = 312 and 312 +- 1 are primes, so 7 is a term.

%t lst={};Do[p1=Prime[n];p2=Prime[n+1];d=p2-p1;a=p1*p2*d+d;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p1]],{n,7!}];lst

%Y Cf. A099349, A153374, A153375, A153377.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 24 2008