A248739 a(n) = 29*n + ceiling(n/29).

0, 30, 59, 88, 117, 146, 175, 204, 233, 262, 291, 320, 349, 378, 407, 436, 465, 494, 523, 552, 581, 610, 639, 668, 697, 726, 755, 784, 813, 842, 872, 901, 930, 959, 988, 1017, 1046, 1075, 1104, 1133, 1162, 1191, 1220, 1249, 1278, 1307, 1336, 1365, 1394, 1423

Offset: 0

Author

Karl V. Keller, Jr., Oct 13 2014

Keywords

• nonn
• easy

Comments

This is an approximation to A004962 (ceiling of n*phi^7, where phi is the golden ratio, A001622).

Examples

			For n = 10, 29n + ceiling(n/29) = 290 + ceiling(0.3) = 290 + 1 = 291.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 0..1000
• Ron Knott, Fibonacci numbers and the golden section
• Eric Weisstein's World of Mathematics, Golden Ratio
• Wikipedia, Golden ratio
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A001622 (phi), A195819 (29*n).

Cf. A004922 (floor(n*phi^7)), A004962 (ceiling(n*phi^7)), A004942 (round(n*phi^7)).

Programs

Magma

[29*n + Ceiling(n/29): n in [0..60]]; // Vincenzo Librandi, Oct 13 2014

Maple

A248739:=n->29*n+ceil(n/29): seq(A248739(n), n=0..50); # Wesley Ivan Hurt, Oct 14 2014

Mathematica

Table[29 n + Ceiling[n/29], {n, 0, 60}] (* Vincenzo Librandi, Oct 13 2014 *)

Python

from math import *
for n in range(0,101):
  print(n, (29*n+ceil(n/29.0)))

Formula

a(n) = 29*n + ceiling(n/29).

a(n) = A004962(n) for n < 871. - Joerg Arndt, Oct 18 2014