A153405 Larger of 3 consecutive prime numbers such that p1*p2*p3 + d1 + d2 - 1 = average of twin prime pairs, d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

7, 577, 1759, 5119, 6959, 9293, 11057, 14407, 24877, 25183, 26209, 31177, 34483, 41729, 42403, 45293, 61121, 62539, 80621, 82153, 90007, 91997, 92353, 93827, 98387, 98893, 103613, 105913, 111409, 117163, 121001, 122833, 128431, 135613

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Keywords

• nonn

Examples

			7 is a term since (3, 5, 7) are consecutive primes, 3*5*7 + 2 + 2 - 1 = 108, and 108 +-1 = are twin primes.
		

Links

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

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404.

Programs

Magma

[p3:k in [1..14000]| IsPrime(p1*p2*p3+p3-p1-2) and IsPrime(p1*p2*p3+p3-p1) where p1 is NthPrime(k) where p2 is NthPrime(k+1) where p3 is NthPrime(k+2) ]; // Marius A. Burtea, Dec 31 2019

Mathematica

lst = {}; Do[p1 = Prime[n]; p2 = Prime[n + 1]; p3 = Prime[n + 2]; d1 = p2 -p1; d2 = p3 - p2; a = p1 * p2 * p3 + d1 + d2 - 1; If[PrimeQ[a - 1] && PrimeQ[a + 1], AppendTo[lst, p3]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky *)
okQ[{a_, b_, c_}] := Module[{x = a b c + (b - a) + (c - b) - 1}, PrimeQ[x - 1] && PrimeQ[x + 1]]
Transpose[Select[Partition[Prime[Range[15000]], 3, 1], okQ]][[3]] (* Harvey P. Dale, Jan 18 2011 *)