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

%I A375182 #13 Sep 28 2024 07:36:46
%S A375182 4,6,9,10,14,21,26,34,46,55,65,82,93,106,121,141,155,161,177,201,219,
%T A375182 247,274,295,314,339,361,391,417,446,469,501,535,566,611,649,685,718,
%U A375182 753,793,835,878,917,958,995,1041,1094,1138,1186,1238,1285,1339,1389,1438,1497,1555,1618,1673,1735,1795,1851
%N A375182 Slowest increasing sequence of semiprimes such that the differences of successive terms are distinct.
%C A375182 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.
%H A375182 Robert Israel, <a href="/A375182/b375182.txt">Table of n, a(n) for n = 1..10000</a>
%p A375182 R:= 4: x:= 4: S:= {}: count:= 1:
%p A375182 for i from 6 while count < 100 do
%p A375182   if not member(i-x, S) and numtheory:-bigomega(i) = 2 then
%p A375182     R:= R,i; S:= S union {i-x}; x:= i; count:= count+1
%p A375182   fi
%p A375182 od:
%p A375182 R;
%t A375182 s = {4, 6};  df  = {2}; Do[k = 1; While [MemberQ[df, k] ||
%t A375182 2 != PrimeOmega[a = s[[-1]] + k], k++]; AppendTo[s, a]; AppendTo[df, k], {98}];
%t A375182 s
%Y A375182 Cf. A001358, A084758.
%K A375182 nonn
%O A375182 1,1
%A A375182 _Zak Seidov_ and _Robert Israel_, Sep 23 2024