A071415 Maximal m such that all numbers in [0,m] are expressible as a*b + c with a + c <= n, b <= n and a,b,c nonnegative integers.

1, 4, 7, 10, 17, 22, 32, 38, 51, 66, 75, 93, 113, 124, 147, 172, 199, 214, 244, 276, 310, 328, 365, 404, 445, 488, 511, 557, 605, 655, 707, 734, 789, 846, 905, 966, 1029, 1062, 1128, 1196, 1266, 1338, 1412, 1450, 1527, 1606, 1687, 1770, 1855, 1942, 1987, 2077

Offset

1,2

Comments

a(n)/n^2 seems to tend to 1 as n tends to infinity.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Example

a(3)=7 because 1 = 0*3 + 1, 2 = 0*3 + 2, 3 = 0*3 + 3, 4 = 1*3 + 1, 5 = 1*3 + 2, 6 = 2*3 + 0, 7 = 2*3 + 1 and 8 is not expressible in that form.

Crossrefs

Sequence in context: A310716 A310717 A119249 * A310718 A310719 A103408

Adjacent sequences: A071412 A071413 A071414 * A071416 A071417 A071418

Keyword

nonn

Author

Sascha Kurz, May 29 2002

Extensions

Name corrected by Sean A. Irvine, Jul 17 2024

Status

approved