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A249079
a(n) = 29*n + floor( n/29 ) + 0^( 1-floor( (14+(n mod 29))/29 ) ).
3
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
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
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., Oct 20 2014
STATUS
approved