A249079 - OEIS

%I #45 Apr 03 2024 11:03:56

%S 0,29,58,87,116,145,174,203,232,261,290,319,348,377,406,436,465,494,

%T 523,552,581,610,639,668,697,726,755,784,813,842,871,900,929,958,987,

%U 1016,1045,1074,1103,1132,1161,1190,1219,1248,1278,1307,1336

%N a(n) = 29*n + floor( n/29 ) + 0^( 1-floor( (14+(n mod 29))/29 ) ).

%C This is an approximation to A004942 (Nearest integer to n*phi^7, where phi is the golden ratio, A001622).

%H Karl V. Keller, Jr., <a href="/A249079/b249079.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>

%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, 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).

%e n= 0, 29*n+floor(0.0) +0^(1-floor(0.48))=    0 +0 +0 =    0 (n/29=0,0^1=0).

%e n=14, 29*n+floor(0.48)+0^(1-floor(0.97))=  406 +0 +0 =  406 (0^1=0).

%e n=15, 29*n+floor(0.52)+0^(1-floor(1.0)) =  435 +0 +1 =  436 (0^0=1).

%e n=28, 29*n+floor(0.97)+0^(1-floor(1.45))=  812 +0 +1 =  813 (0^0=1).

%e n=29, 29*n+floor(1.0) +0^(1-floor(0.48))=  841 +1 +0 =  842 (n/29*1,0^1=0).

%e n=43, 29*n+floor(1.48)+0^(1-floor(0.97))= 1247 +1 +0 = 1248 (0^1=0).

%e n=44, 29*n+floor(1.52)+0^(1-floor(1.0)) = 1276 +1 +1 = 1278 (0^0=1).

%e n=58, 29*n+floor(2.0) +0^(1-floor(0.48))= 1682 +2 +0 = 1684 (n/29*2,0^1=0).

%e n=85, 29*n+floor(2.93)+0^(1-floor(1.41))= 2465 +2 +1 = 2468 (0^0=1).

%e n=86, 29*n+floor(2.97)+0^(1-floor(1.45))= 2494 +2 +1 = 2497 (0^0=1).

%e n=87, 29*n+floor(3.0) +0^(1-floor(0.48))= 2523 +3 +0 = 2526 (n/29*3,0^0=0).

%o (Python)

%o for n in range(101):

%o     print(29*n+n//29+0**(1-(14+n%29)//29), end=', ')

%o (Python)

%o def A249079(n):

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

%o     return 29*n+a+int(b>=15) # _Chai Wah Wu_, Jul 27 2022

%o (PARI) a(n) = 29*n + n\29 + 0^(1 - (14+(n % 29))\29); \\ _Michel Marcus_, Oct 25 2014

%o (Magma) [29*n + Floor(n/29) + 0^(1-Floor((14+(n mod 29))/29)) : n in [0..50]]; // _Vincenzo Librandi_, Nov 05 2014

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

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

%K nonn

%O 0,2

%A _Karl V. Keller, Jr._, Oct 20 2014