%I #48 Jul 28 2022 09:06:14

%S 0,29,58,87,116,145,174,203,232,261,290,319,348,377,406,435,464,493,

%T 522,551,580,609,638,667,696,725,754,783,812,841,871,900,929,958,987,

%U 1016,1045,1074,1103,1132,1161,1190,1219,1248

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

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

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

%H Karl V. Keller, Jr., <a href="/A248786/b248786.txt">Table of n, a(n) for n = 0..1000</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/">Fibonacci numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Golden_ratio">Golden ratio</a>

%e For n = 0, 29*n + floor(0.0) + 0^0 - 0^(0) = 0 + 0 + 1 - 1 = 0 (n=29*0).

%e For n = 28, 29*n + floor(0.97) + 0^28 - 0^(28)= 812 + 0 + 0 - 0 = 812.

%e For n = 29, 29*n + floor(1.0) + 0^29 - 0^(0) = 841 + 1 + 0 - 1 = 841 (n=29*1).

%e For n = 31, 29*n + floor(1.1) + 0^31 - 0^(2) = 899 + 1 + 0 - 0 = 900.

%e For n = 87, 29*n + floor(3.0) + 0^87 - 0^(0) = 2523 + 3 + 0 - 1 = 2525 (n=29*3).

%o (Python)

%o from math import *

%o from decimal import *

%o getcontext().prec = 100

%o for n in range(0,101):

%o ..print n,(29*n+floor(n/29.0))+ 0**n-0**(n%29)

%o (Python)

%o def A248786(n):

%o a, b = divmod(n,29)

%o return 29*n+a-int(not b) if n else 0 # _Chai Wah Wu_, Jul 27 2022

%o (Magma) [(29*n+Floor(n/29))+ 0^n-0^(n mod 29): n in [0..60]]; // _Vincenzo Librandi_, Oct 14 2014

%o (PARI) a(n) = 29*n+ n\29 + 0^n - 0^(n % 29); \\ _Michel Marcus_, Oct 14 2014

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

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

%K nonn,easy

%O 0,2

%A _Karl V. Keller, Jr._, Oct 14 2014