A365833 - OEIS

%I #8 Sep 25 2023 08:15:54

%S 130,195,222,292,498,582,670,814,970,1362,1398,1534,1645,1813,1834,

%T 1978,2514,2717,2853,2865,2994,3092,3130,3157,3211,3462,3897,4527,

%U 4615,4707,4782,5529,6070,6610,7270,7399,7414,7527,7767,8029,8305,8687,8911,9994,10330,10390,11297,11557,11619,11679

%N Triprimes a such that, if b is the next triprime, a + b and b - a are also triprimes.

%C It appears that in most cases b - a = 8.

%H Robert Israel, <a href="/A365833/b365833.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 222 ix a term because 222 = 2*3*37 is a triprime, the next triprime is 230 = 2  5 * 23, and 222 + 230 = 452 = 2^2 * 113 and 230 - 222 = 8 = 2^3 are triprimes.

%p with(priqueue);

%p a:= 8:  R:= NULL: count:= 0:

%p initialize(triprimes);

%p insert([-8,0,2],triprimes);

%p while count < 50 do

%p     v:= extract(triprimes);

%p     if v[2] = 3 then

%p       b:= -v[1];

%p       if numtheory:-bigomega(b-a) = 3 and numtheory:-bigomega(b+a)=3 then

%p         R:= R, a; count:= count+1

%p       fi;

%p       a:= b;

%p     else

%p       insert(v+[0,1,0],triprimes);

%p       q:= nextprime(v[3]);

%p       w:= v[1]*(q/v[3])^(3-v[2]);

%p       insert([w,v[2],q],triprimes)

%p     fi

%p od:

%p R;

%t Select[Partition[Select[Range[12000], PrimeOmega[#] == 3 &], 2, 1], AllTrue[{#1 + #2, #2 - #1}, PrimeOmega[#] == 3 &] & @@ # &][[All, 1]] (* _Michael De Vlieger_, Sep 20 2023 *)

%Y Cf. A014612.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Sep 19 2023