%I #4 Jun 19 2021 12:53:57

%S 1,4,15,28,39,50,81,350,459,512,675,944,987,1040,1917,1936,2325,2378,

%T 2421,2588,2745,2812,3459,3488,3495,3506,5667,5804,6027,6074,24765,

%U 24832,25479,25552,27621,27848,27951,27980,34101,34720,34773,35344

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

%C 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, ...

%t 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

%Y Cf. A154484, A154485, A154486, A154487, A154488

%K nonn

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009

%E NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021