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

1,1

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

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

Crossrefs

Cf. A001358, A084758.

Sequence in context: A054395 A142863 A318990 * A132435 A108631 A200677

Adjacent sequences: A375178 A375179 A375180 * A375183 A375184 A375185

Keyword

nonn

Author

Zak Seidov and Robert Israel, Sep 23 2024

Status

approved