A270296 Numbers which are representable as a sum of five but no fewer consecutive nonnegative integers.

20, 40, 80, 100, 140, 160, 200, 220, 260, 280, 320, 340, 380, 400, 440, 460, 500, 520, 560, 580, 620, 640, 680, 700, 740, 760, 800, 820, 860, 880, 920, 940, 980, 1000, 1040, 1060, 1100, 1120, 1160, 1180, 1220, 1240, 1280, 1300, 1340, 1360, 1400, 1420, 1460

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

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

Formula

A163169(a(n)) = 5. - Ray Chandler, Mar 22 2016

a(n) = 20*A001651(n). - Hugo Pfoertner, Feb 04 2021

G.f.: 20*x*(1 + x + x^2)/((1 - x)*(1 - x^2)). - Andrew Howroyd, Oct 31 2025

Example

15 = 1 + 2 + 3 + 4 + 5 = 7 + 8 (not in sequence);
20 = 2 + 3 + 4 + 5 + 6;
40 = 6 + 7 + 8 + 9 + 10;
80 = 14 + 15 + 16 + 17 + 18.

Mathematica

LinearRecurrence[{1, 1, -1}, {20, 40, 80}, 50] (* Harvey P. Dale, Jan 11 2026 *)

Prog

(PARI) a(n)=20+((n-1)\2)*60+[0, 20][(n-1)%2+1] \\ Charles R Greathouse IV, May 12 2026

Crossrefs

Cf. A001651, A138591, A270297, A270298, A270299, A270300, A270301, A270302, A270303.

Sequence in context: A008602 A061830 A235282 * A338433 A347368 A041790

Adjacent sequences: A270293 A270294 A270295 * A270297 A270298 A270299

Keyword

nonn,easy

Author

Martin Renner, Mar 14 2016

Status

approved