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

1,2

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

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

Crossrefs

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

Sequence in context: A128243 A219294 A338747 * A130278 A024080 A099436

Adjacent sequences: A154491 A154492 A154493 * A154495 A154496 A154497

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Extensions

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

Status

approved