A154666 -id:A154666 - cp's OEIS frontend

A154667 Averages of twin prime pairs such that p1 * p2 + AverageTwinPrime is prime.

4, 6, 30, 60, 138, 180, 240, 420, 618, 1050, 1608, 1698, 1788, 2268, 2310, 2730, 3258, 3390, 3528, 3768, 4158, 4218, 4338, 4800, 5640, 5868, 6660, 6690, 6870, 6960, 7488, 7548, 7590, 8538, 8628, 8970, 9630, 9858, 9930, 10458, 11118, 11970, 12540, 13338

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

nonn

			3*5 + 4 = 19.
5*7 + 6 = 41.

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

Cf. A154666.

A014574 INTERSECT A045546. - R. J. Mathar, May 31 2010

[p+1:p in PrimesUpTo(14000)|IsPrime(p+2) and IsPrime(p*(p+2)+p+1)]; // Marius A. Burtea, Dec 21 2019

lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],If[PrimeQ[(n-1)*(n+1)+n],AppendTo[lst,n]]],{n,8!}];lst

A154668 Averages of twin primes such that p1*p2 -+ AverageTwinPrime are primes.

Original entry on oeis.org

4, 6, 60, 420, 2730, 8970, 11970, 21840, 28620, 29130, 44130, 48120, 55050, 56100, 61980, 74160, 84390, 87540, 111270, 111870, 143880, 176550, 191670, 207510, 227610, 229590, 233550, 251220, 258330, 281580, 324450, 343770, 356820, 390000

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

nonn

			3*5 - 4 = 11 and 3*5 + 4 = 19.
5*7 - 6 = 29 and 5*7 + 6 = 41.

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

Cf. A014574, A154666, A154667.

[NthPrime(k)+1:k in [1..35000]|IsPrime(NthPrime(k)+2) and forall{s:s in [1+NthPrime(k),-1-NthPrime(k)]|IsPrime(NthPrime(k)*NthPrime(k+1)+s)}]; // Marius A. Burtea, Dec 22 2019

lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],If[PrimeQ[(n-1)*(n+1)-n]&&PrimeQ[(n-1)*(n+1)+n],AppendTo[lst,n]]],{n,2*9!}];lst

cp's OEIS Frontend

A154667 Averages of twin prime pairs such that p1 * p2 + AverageTwinPrime is prime.

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