A249079 a(n) = 29*n + floor( n/29 ) + 0^( 1-floor( (14+(n mod 29))/29 ) ).

0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 436, 465, 494, 523, 552, 581, 610, 639, 668, 697, 726, 755, 784, 813, 842, 871, 900, 929, 958, 987, 1016, 1045, 1074, 1103, 1132, 1161, 1190, 1219, 1248, 1278, 1307, 1336

Offset

0,2

Comments

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

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

Index entries for linear recurrences with constant coefficients, 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).

Example

n= 0, 29*n+floor(0.0) +0^(1-floor(0.48))=    0 +0 +0 =    0 (n/29=0,0^1=0).
n=14, 29*n+floor(0.48)+0^(1-floor(0.97))=  406 +0 +0 =  406 (0^1=0).
n=15, 29*n+floor(0.52)+0^(1-floor(1.0)) =  435 +0 +1 =  436 (0^0=1).
n=28, 29*n+floor(0.97)+0^(1-floor(1.45))=  812 +0 +1 =  813 (0^0=1).
n=29, 29*n+floor(1.0) +0^(1-floor(0.48))=  841 +1 +0 =  842 (n/29*1,0^1=0).
n=43, 29*n+floor(1.48)+0^(1-floor(0.97))= 1247 +1 +0 = 1248 (0^1=0).
n=44, 29*n+floor(1.52)+0^(1-floor(1.0)) = 1276 +1 +1 = 1278 (0^0=1).
n=58, 29*n+floor(2.0) +0^(1-floor(0.48))= 1682 +2 +0 = 1684 (n/29*2,0^1=0).
n=85, 29*n+floor(2.93)+0^(1-floor(1.41))= 2465 +2 +1 = 2468 (0^0=1).
n=86, 29*n+floor(2.97)+0^(1-floor(1.45))= 2494 +2 +1 = 2497 (0^0=1).
n=87, 29*n+floor(3.0) +0^(1-floor(0.48))= 2523 +3 +0 = 2526 (n/29*3,0^0=0).

Prog

(Python)
for n in range(101):
    print(29*n+n//29+0**(1-(14+n%29)//29), end=', ')
(Python)
def A249079(n):
    a, b = divmod(n, 29)
    return 29*n+a+int(b>=15) # Chai Wah Wu, Jul 27 2022
(PARI) a(n) = 29*n + n\29 + 0^(1 - (14+(n % 29))\29); \\ Michel Marcus, Oct 25 2014
(Magma) [29*n + Floor(n/29) + 0^(1-Floor((14+(n mod 29))/29)) : n in [0..50]]; // Vincenzo Librandi, Nov 05 2014

Crossrefs

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

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

Sequence in context: A195819 A248786 A004922 * A004942 A033904 A184073

Adjacent sequences: A249076 A249077 A249078 * A249080 A249081 A249082

Keyword

nonn

Author

Karl V. Keller, Jr., Oct 20 2014

Status

approved