A248786 a(n) = 29*n + floor(n/29) + 0^n - 0^(n mod 29).

0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 435, 464, 493, 522, 551, 580, 609, 638, 667, 696, 725, 754, 783, 812, 841, 871, 900, 929, 958, 987, 1016, 1045, 1074, 1103, 1132, 1161, 1190, 1219, 1248

Offset: 0

Author

Karl V. Keller, Jr., Oct 14 2014

Keywords

• nonn
• easy

Comments

This is an approximation to A004922 (floor of n*phi^7, where phi is the golden ratio, A001622).

The "+ 0^n - 0^(n mod 29)" corrects a(n), for n=0 and multiples of 29. (See examples below.)

Examples

			For n = 0,  29*n + floor(0.0)  + 0^0  - 0^(0) =   0  + 0  + 1  - 1 = 0 (n=29*0).
For n = 28, 29*n + floor(0.97) + 0^28 - 0^(28)= 812  + 0  + 0  - 0 = 812.
For n = 29, 29*n + floor(1.0)  + 0^29 - 0^(0) = 841  + 1  + 0  - 1 = 841 (n=29*1).
For n = 31, 29*n + floor(1.1)  + 0^31 - 0^(2) = 899  + 1  + 0  - 0 = 900.
For n = 87, 29*n + floor(3.0)  + 0^87 - 0^(0) = 2523 + 3  + 0  - 1 = 2525 (n=29*3).
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 0..1000
• Ron Knott, Fibonacci numbers
• Eric Weisstein's World of Mathematics, Golden Ratio
• Wikipedia, Golden ratio

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+Floor(n/29))+ 0^n-0^(n mod 29): n in [0..60]]; // Vincenzo Librandi, Oct 14 2014

PARI

a(n) = 29*n+ n\29 + 0^n - 0^(n % 29); \\ Michel Marcus, Oct 14 2014

Python

from math import *
from decimal import *
getcontext().prec = 100
for n in range(0,101):
  print(n, (29*n+floor(n/29.0))+ 0**n-0**(n%29))

Python

def A248786(n):
    a, b = divmod(n,29)
    return 29*n+a-int(not b) if n else 0 # Chai Wah Wu, Jul 27 2022