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

2, 9, 20, 33, 40, 141, 298, 435, 536, 687, 884, 1197, 1244, 1665, 1792, 2235, 2486, 2595, 2602, 3765, 3784, 4095, 4148, 4605, 4868, 5061, 5330, 6159, 6220, 6579, 6662, 7119, 7162, 7341, 8288, 10791, 11438, 11859, 12142, 12825, 13274, 14553, 14734

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 : 9-2=7;9+2=11;9*2=18, ...

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

A:= 2,9: b:= 9:
for i from 3 to 100 do
  p:= 2:
  do
    p:= nextprime(p);
    k:= b + p;
    if isprime(b*k+1) and isprime(b*k-1) and isprime(k+b) then
       A:= A,k; b:= k; break
fi od od:
A; # Robert Israel, Jan 01 2024

Mathematica

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

Extensions

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