A279858 Next term is uniquely the sum of 4 earlier terms.

1, 2, 4, 8, 15, 22, 26, 28, 36, 37, 41, 98, 117, 120, 124, 214, 222, 226, 236, 333, 338, 532, 533, 534, 538, 541, 543, 544, 743, 746, 956, 957, 958, 961, 1054, 1263, 1267, 1463, 1466, 1468, 1473, 1474, 1475, 1476, 1684, 1894, 2196, 2198, 2199, 2205, 2206, 2404, 2406, 2408, 2411

Offset: 1

Author

Robert G. Wilson v, Dec 20 2016

Keywords

• nonn
• easy

Comments

With a(1)=1, a(2)=2, a(3)=4, a(4)=8 and for n>4, a(n) = least number which is a unique sum of four distinct earlier terms.

Written this way, we see that this sequence is to 4 as A007087 is to 3 and A002858 (Ulam numbers) is to 2.

Crossrefs

Cf. A002858, A007086, A007087.

Programs

Mathematica

a[n_ /; n <= 4] := 2^(n - 1); a[n_] := a[n] = (t = Table[a[i] + a[j] + a[k] + a[l], {i, 1, n - 4}, {j, i + 1, n - 3}, {k, j + 1, n - 2}, {l, k + 1, n - 1}] // Flatten; Complement[ Select[t // Tally, #[[2]] == 1 &][[All, 1]], Array[a, n - 1]] // Sort // First); Array[a, 55] (* after Jean-François Alcover A007086 *)