cp's OEIS Frontend

A254043 a(n) is the smallest number not already used such that the sum of the first n terms is semiprime.

%I A254043 #33 Jan 08 2025 11:05:42
%S A254043 4,2,3,1,5,6,12,13,9,7,15,8,10,11,16,19,14,22,17,20,21,18,25,23,26,28,
%T A254043 27,29,34,24,32,36,42,35,41,30,33,31,40,46,43,39,38,48,44,47,45,50,37,
%U A254043 56,51,49,55,60,58,63,53,64,62,52,54,66,57,69,70,80,61,68,59,65,71,72,81,76,83
%N A254043 a(n) is the smallest number not already used such that the sum of the first n terms is semiprime.
%C A254043 Is this a permutation of the natural numbers? - _Derek Orr_, Feb 07 2015
%e A254043 a(3) = 3 because 3 is the smallest number not already used such that the sum of all 3 terms (4 + 2 + 3 = 9) is semiprime.
%p A254043 N:= 1000: # get all terms before the first term > N
%p A254043 S:= {$1..N} minus {4}:
%p A254043 T:= 4: A[1]:= 4:
%p A254043 for n from 2 do
%p A254043   found:= false;
%p A254043   for s in S do
%p A254043     if numtheory:-bigomega(s+T) = 2 then
%p A254043        A[n]:= s;
%p A254043        S:= S minus {s};
%p A254043        T:= s + T;
%p A254043        found:= true;
%p A254043        break
%p A254043     fi
%p A254043   od:
%p A254043   if not found then break fi;
%p A254043 od:
%p A254043 seq(A[i],i=1..n-1); # _Robert Israel_, Mar 24 2015
%t A254043 f[n_] := Block[{k, s = Select[Range[2(n^2 + n)/3], PrimeOmega@ # == 2 &], t = Table[4, {n}]}, For[k = 2, k <= n, k++, t[[k]] = Min@ Select[s - Total[Take[t, k - 1]], # > 0 && ! MemberQ[t, #] &]]; t]; f@ 75 (* _Michael De Vlieger_, Mar 24 2015 *)
%o A254043 (PARI) v=[4];n=1;while(n<100,if(bigomega(vecsum(v)+n)==2&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Feb 07 2015
%Y A254043 Cf. A001358, A054408, A287662.
%K A254043 nonn,easy
%O A254043 1,1
%A A254043 _G. L. Honaker, Jr._, Jan 23 2015