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A154494
a(n+1) -+ a(n) = prime, a(n+1)*a(n) = average of twin prime pairs, a(1)=1, a(2)=6.
8
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
NAME adapted to offset. - R. J. Mathar, Jun 19 2021
STATUS
approved