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A154495 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=2,a(2)=9.

%I A154495 #9 Jan 02 2024 00:49:24
%S A154495 2,9,20,33,40,141,298,435,536,687,884,1197,1244,1665,1792,2235,2486,
%T A154495 2595,2602,3765,3784,4095,4148,4605,4868,5061,5330,6159,6220,6579,
%U A154495 6662,7119,7162,7341,8288,10791,11438,11859,12142,12825,13274,14553,14734
%N A154495 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=2,a(2)=9.
%C A154495 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 : 9-2=7;9+2=11;9*2=18, ...
%H A154495 Robert Israel, <a href="/A154495/b154495.txt">Table of n, a(n) for n = 1..10000</a>
%p A154495 A:= 2,9: b:= 9:
%p A154495 for i from 3 to 100 do
%p A154495   p:= 2:
%p A154495   do
%p A154495     p:= nextprime(p);
%p A154495     k:= b + p;
%p A154495     if isprime(b*k+1) and isprime(b*k-1) and isprime(k+b) then
%p A154495        A:= A,k; b:= k; break
%p A154495 fi od od:
%p A154495 A; # _Robert Israel_, Jan 01 2024
%t A154495 a=2;b=9;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 A154495 Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494
%K A154495 nonn
%O A154495 1,1
%A A154495 _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009
%E A154495 NAME adapted to offset. - _R. J. Mathar_, Jun 19 2021