A366693 Contribution to the OEIS

 

A366693 Minimal number of primorials or their negatives that add to n. 2

0, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 3, 2, 3, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 4, 3, 4, 4, 4, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 5, 4, 5, 5, 6, 6, 6, 5, 6, 6, 6, 5, 5, 4, 5, 5, 5 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 EXAMPLE 5 = 6 - 1 (two primorials), so a(5) = 2. 27 = 30 - 2 - 1 (three primorials), so a(27) = 3. MATHEMATICA a[nthPrimorials_Integer?NonNegative (* Increase nthPrimorials to use more positive and negative primorials in sum *), numberOfPrimorials_Integer?NonNegative (* Increase numberOfPrimorials to increase cap of minimal number of primorials *)] := a[nthPrimorials, numberOfPrimorials] = Module[{A002110, f, h, s}, A002110[nthPrimorials] = Join[{1}, Denominator[Accumulate[1/Prime[Range[nthPrimorials]]]]]; A002110[n_] := A002110[n] = Join[{1}, Denominator[Accumulate[1/Prime[Range[n]]]]]; f[n_] := f[n] = Flatten[Table[p*r, {p, A002110[n - 1]}, {r, {1, -1}}]]; h[n_, u_] := h[n, u] = Sort[Select[DeleteDuplicates[Flatten[Table[Sum[p[j], {j, 1, u}], ##] & @@ Table[{p[j], f[n]}, {j, 1, u}]]], # > 0 &]]; s = Table[Infinity, {A002110[nthPrimorials][[-1]]}]; Monitor[Do[If[s[[k]] > k, s[[k]] = l], {l, 1, numberOfPrimorials}, {k, h[nthPrimorials, l]}], {l, k}]; s = Join[{0}, s]; If[MemberQ[s, Infinity], s[[1 ;; Position[s, Infinity][[1, 1]] - 1]], s]]; a[6, 6] (* Robert P. P. McKone, Oct 21 2023 *) CROSSREFS Cf. A002110, A276150, A366136. Sequence in context: A261915 A109037 A366136 * A147680 A192895 A210685 Adjacent sequences: A366690 A366691 A366692 * A366694 A366695 A366696 KEYWORD nonn,look AUTHOR James C. McMahon, Oct 16 2023 STATUS approved