A154494 a(n+1) -+ a(n) = prime, a(n+1)*a(n) = average of twin prime pairs, a(1)=1, a(2)=6.

1, 6, 17, 84, 247, 300, 341, 720, 767, 834, 913, 960, 989, 1590, 1741, 2772, 2945, 3102, 3451, 3540, 3563, 4020, 4159, 4812, 5431, 5700, 6131, 6192, 6245, 8586, 9373, 10056, 10163, 10314, 10543, 10944, 11033, 11844, 12055, 13566, 14015, 15048, 15155

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 : 6-1=5; 6+1=7; 6*1=6, 17-6=11; 17+6=23; 17*6=102, ... .

Links

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

Crossrefs

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

Programs

Maple

f:= proc(x) local k;
  for k from x+1 by 2 do
    if isprime(k+x) and isprime(k-x) and isprime(k*x-1) and isprime(k*x+1) then return k fi
  od;
end proc:
R:= 1,6: x:= 6:
for count from 3 to 100 do
  x:= f(x);
  R:= R,x
od:
R; # Robert Israel, Nov 29 2023

Mathematica

a=1;b=6;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