A365833 Triprimes a such that, if b is the next triprime, a + b and b - a are also triprimes.

130, 195, 222, 292, 498, 582, 670, 814, 970, 1362, 1398, 1534, 1645, 1813, 1834, 1978, 2514, 2717, 2853, 2865, 2994, 3092, 3130, 3157, 3211, 3462, 3897, 4527, 4615, 4707, 4782, 5529, 6070, 6610, 7270, 7399, 7414, 7527, 7767, 8029, 8305, 8687, 8911, 9994, 10330, 10390, 11297, 11557, 11619, 11679

Offset

1,1

Comments

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

Links

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

Example

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.

Maple

with(priqueue);
a:= 8:  R:= NULL: count:= 0:
initialize(triprimes);
insert([-8, 0, 2], triprimes);
while count < 50 do
    v:= extract(triprimes);
    if v[2] = 3 then
      b:= -v[1];
      if numtheory:-bigomega(b-a) = 3 and numtheory:-bigomega(b+a)=3 then
        R:= R, a; count:= count+1
      fi;
      a:= b;
    else
      insert(v+[0, 1, 0], triprimes);
      q:= nextprime(v[3]);
      w:= v[1]*(q/v[3])^(3-v[2]);
      insert([w, v[2], q], triprimes)
    fi
od:
R;

Mathematica

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

Crossrefs

Cf. A014612.

Sequence in context: A248649 A050238 A115937 * A298381 A299248 A299457

Adjacent sequences: A365830 A365831 A365832 * A365834 A365835 A365836

Keyword

nonn

Author

Zak Seidov and Robert Israel, Sep 19 2023

Status

approved