A254043 a(n) is the smallest number not already used such that the sum of the first n terms is semiprime.
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, 27, 29, 34, 24, 32, 36, 42, 35, 41, 30, 33, 31, 40, 46, 43, 39, 38, 48, 44, 47, 45, 50, 37, 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
Offset: 1
Examples
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.
Programs
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Maple
N:= 1000: # get all terms before the first term > N S:= {$1..N} minus {4}: T:= 4: A[1]:= 4: for n from 2 do found:= false; for s in S do if numtheory:-bigomega(s+T) = 2 then A[n]:= s; S:= S minus {s}; T:= s + T; found:= true; break fi od: if not found then break fi; od: seq(A[i],i=1..n-1); # Robert Israel, Mar 24 2015 -
Mathematica
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 *) -
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
Comments