A100764 a(1) = 1, a(2) = 2, a(3) = 3, a(n) = least number not the sum of three or fewer previous terms.

1, 2, 3, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325

Offset

1,2

Comments

Generalization: let the first k terms of the sequence be 1,2,...,k, and for n > k, let b(n) be defined as the least positive integer that is not the sum of k or fewer previous terms; then b(n+k) = b(n) + n* k(k+1)/2. b(n) = (n+1)*k*(k+1)/2 + 1. n > k. Here a(n) is for k=3.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2, -1).

Formula

a(n+4) = a(4) + 6n for n > 4; a(n) = 6n - 17, n >3.

From Chai Wah Wu, Oct 25 2018: (Start)

a(n) = 2*a(n-1) - a(n-2) for n > 5.

G.f.: x*(2*x^4 + 3*x^3 + 1)/(x - 1)^2. (End)

Mathematica

a[1] = 1; a[2] = 2; a[3] = 3; a[n_] := a[n] = (m = 1; l = n - 1; t = Union[ Flatten[ Join[ Table[ a[i], {i, l}], Table[ a[i] + a[j], {i, l}, {j, i + 1, l}], Table[ a[i] + a[j] + a[k], {i, l}, {j, i + 1, l}, {k, j + 1, l}] ]]]; While[ Position[t, m] != {}, m++ ]; m); Table[ a[n], {n, 60}] (* Robert G. Wilson v, Dec 14 2004 *)
LinearRecurrence[{2, -1}, {1, 2, 3, 7, 13}, 60] (* Harvey P. Dale, Nov 17 2024 *)

Crossrefs

Essentially the same as A016921.

Sequence in context: A105792 A130903 A068828 * A076974 A051484 A101415

Adjacent sequences: A100761 A100762 A100763 * A100765 A100766 A100767

Keyword

easy,nonn

Author

Amarnath Murthy, Nov 25 2004

Extensions

More terms from Robert G. Wilson v, Dec 14 2004

Status

approved