A153376 Smaller of two consecutive prime numbers such that p1*p2*d + d = average of twin prime pairs, d (delta) = p2 - p1.

5, 7, 41, 43, 101, 103, 113, 227, 331, 379, 569, 647, 733, 751, 863, 971, 1093, 1123, 1163, 1217, 1381, 1499, 2063, 2131, 2179, 2311, 2357, 2399, 2707, 2711, 3709, 4789, 4817, 5021, 5051, 5171, 5479, 5501, 5987, 6011, 6827, 6949, 6967, 7103, 7213, 7477

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 24 2008

Keywords

• nonn

Comments

See A153377 for the corresponding larger prime.

Examples

			5*7*2 + 2 = 72 and 72 +- 1 are primes, so 5 is a term.
7*11*4 + 4 = 312 and 312 +- 1 are primes, so 7 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A099349, A153374, A153375, A153377.

Programs

Mathematica

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