A375182 Slowest increasing sequence of semiprimes such that the differences of successive terms are distinct.

4, 6, 9, 10, 14, 21, 26, 34, 46, 55, 65, 82, 93, 106, 121, 141, 155, 161, 177, 201, 219, 247, 274, 295, 314, 339, 361, 391, 417, 446, 469, 501, 535, 566, 611, 649, 685, 718, 753, 793, 835, 878, 917, 958, 995, 1041, 1094, 1138, 1186, 1238, 1285, 1339, 1389, 1438, 1497, 1555, 1618, 1673, 1735, 1795, 1851

Offset: 1

Author

Zak Seidov and Robert Israel, Sep 23 2024

Keywords

• nonn

Comments

For n >= 2, a(n) is the least semiprime k > a(n-1) such that k - a(n-1) <> a(j) - a(j-1) for j < n.

Links

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

Crossrefs

Cf. A001358, A084758.

Programs

Maple

R:= 4: x:= 4: S:= {}: count:= 1:
for i from 6 while count < 100 do
  if not member(i-x, S) and numtheory:-bigomega(i) = 2 then
    R:= R,i; S:= S union {i-x}; x:= i; count:= count+1
  fi
od:
R;

Mathematica

s = {4, 6};  df  = {2}; Do[k = 1; While [MemberQ[df, k] ||
2 != PrimeOmega[a = s[[-1]] + k], k++]; AppendTo[s, a]; AppendTo[df, k], {98}];
s