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

%I A248786 #54 Jun 06 2025 12:39:01
%S A248786 0,29,58,87,116,145,174,203,232,261,290,319,348,377,406,435,464,493,
%T A248786 522,551,580,609,638,667,696,725,754,783,812,841,871,900,929,958,987,
%U A248786 1016,1045,1074,1103,1132,1161,1190,1219,1248
%N A248786 a(n) =  29*n + floor(n/29) + 0^n - 0^(n mod 29).
%C A248786 This is an approximation to A004922 (floor of n*phi^7, where phi is the golden ratio, A001622).
%C A248786 The "+ 0^n - 0^(n mod 29)" corrects a(n), for n=0 and multiples of 29. (See examples below.)
%H A248786 Karl V. Keller, Jr., <a href="/A248786/b248786.txt">Table of n, a(n) for n = 0..1000</a>
%H A248786 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/">Fibonacci numbers</a>
%H A248786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>
%H A248786 Wikipedia, <a href="http://en.wikipedia.org/wiki/Golden_ratio">Golden ratio</a>
%e A248786 For n = 0,  29*n + floor(0.0)  + 0^0  - 0^(0) =   0  + 0  + 1  - 1 = 0 (n=29*0).
%e A248786 For n = 28, 29*n + floor(0.97) + 0^28 - 0^(28)= 812  + 0  + 0  - 0 = 812.
%e A248786 For n = 29, 29*n + floor(1.0)  + 0^29 - 0^(0) = 841  + 1  + 0  - 1 = 841 (n=29*1).
%e A248786 For n = 31, 29*n + floor(1.1)  + 0^31 - 0^(2) = 899  + 1  + 0  - 0 = 900.
%e A248786 For n = 87, 29*n + floor(3.0)  + 0^87 - 0^(0) = 2523 + 3  + 0  - 1 = 2525 (n=29*3).
%o A248786 (Python)
%o A248786 from math import *
%o A248786 from decimal import *
%o A248786 getcontext().prec = 100
%o A248786 for n in range(0,101):
%o A248786   print(n, (29*n+floor(n/29.0))+ 0**n-0**(n%29))
%o A248786 (Python)
%o A248786 def A248786(n):
%o A248786     a, b = divmod(n,29)
%o A248786     return 29*n+a-int(not b) if n else 0 # _Chai Wah Wu_, Jul 27 2022
%o A248786 (Magma) [(29*n+Floor(n/29))+ 0^n-0^(n mod 29): n in [0..60]]; // _Vincenzo Librandi_, Oct 14 2014
%o A248786 (PARI) a(n) = 29*n+ n\29 + 0^n - 0^(n % 29); \\ _Michel Marcus_, Oct 14 2014
%Y A248786 Cf. A001622 (phi), A195819 (29*n).
%Y A248786 Cf. A004922 (floor(n*phi^7)), A004962 (ceiling(n*phi^7)), A004942 (round(n*phi^7)).
%K A248786 nonn,easy
%O A248786 0,2
%A A248786 _Karl V. Keller, Jr._, Oct 14 2014