A154493 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=1,a(2)=4.

1, 4, 15, 28, 39, 50, 81, 350, 459, 512, 675, 944, 987, 1040, 1917, 1936, 2325, 2378, 2421, 2588, 2745, 2812, 3459, 3488, 3495, 3506, 5667, 5804, 6027, 6074, 24765, 24832, 25479, 25552, 27621, 27848, 27951, 27980, 34101, 34720, 34773, 35344

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 : 4-1=3;4+1=5;4*1=4, 15-4=11;15+4=19;15*4=60, ...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488

Programs

Mathematica

a=1;b=4;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