A154496 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=3,a(2)=10.

3, 10, 27, 74, 3093, 3104, 3417, 3580, 3597, 3614, 5907, 5960, 6651, 6962, 9045, 9098, 10479, 10708, 13299, 13382, 14055, 14438, 15099, 16082, 16101, 16112, 16521, 16982, 17505, 19328, 19605, 20062, 22131, 22840, 23013, 23036, 23265, 23422

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

• nonn

Comments

Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 10-3=7;10+3=13;10*3=30, ...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495

Programs

Mathematica

a=3;b=10;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1],AppendTo[lst,n];a=b;b=n],{n,b+1,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021