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

0,2

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.)

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

Example

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).

Prog

(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
(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

Crossrefs

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

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

Sequence in context: A164011 A048846 A195819 * A004922 A249079 A004942

Adjacent sequences: A248783 A248784 A248785 * A248787 A248788 A248789

Keyword

nonn,easy

Author

Karl V. Keller, Jr., Oct 14 2014

Status

approved