A365861 a(1) = 4; for n > 1, a(n) is the first semiprime k not yet listed such that |k - a(n-1)| and k + a(n-1) are also semiprimes.

4, 10, 25, 21, 166, 51, 26, 65, 69, 118, 85, 34, 111, 115, 46, 95, 38, 77, 142, 93, 226, 9, 86, 35, 14, 129, 74, 49, 106, 15, 6, 209, 94, 39, 326, 91, 87, 122, 143, 58, 33, 82, 121, 146, 55, 22, 133, 158, 183, 298, 155, 62, 185, 134, 119, 262, 57, 178, 123, 218, 253, 249, 334, 201, 422, 169, 202

Offset

1,1

Comments

Conjecture: this is a permutation of A001358.

Links

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

Example

a(3) = 25 because 25 = 5^2 is a semiprime, |a(2) - 25| = 15 = 3 * 5 and a(2) + 25 = 35 = 5 * 7 are semiprimes, and 25 is the first semiprime not already in the sequence for which this works.

Maple

R:= 4: a:= 4: S:= select(t -> numtheory:-bigomega(t)=2, [$6..1000]): found:= true:
for n from 2 to 100 while found do
  found:= false;
  for j from 1 to nops(S) do
    b:=S[j];
    if numtheory:-bigomega(abs(b-a)) = 2 and numtheory:-bigomega(a+b) = 2 then
      R:= R, b; a:= b; found:= true; S:= subsop(j=NULL, S);
      break
    fi
od od:
R;

Mathematica

s={m=4}; Do[n=6; While[MemberQ[s, n]|| {2, 2, 2} != PrimeOmega[{n, n-m, n+m}], n++];
AppendTo[s, m=n], {50}]

Crossrefs

Cf. A001358.

Sequence in context: A223014 A038783 A127070 * A107961 A051864 A111153

Adjacent sequences: A365858 A365859 A365860 * A365862 A365863 A365864

Keyword

nonn

Author

Zak Seidov and Robert Israel, Sep 20 2023

Status

approved