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A248786
a(n) = 29*n + floor(n/29) + 0^n - 0^(n mod 29).
2
0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 435, 464, 493, 522, 551, 580, 609, 638, 667, 696, 725, 754, 783, 812, 841, 871, 900, 929, 958, 987, 1016, 1045, 1074, 1103, 1132, 1161, 1190, 1219, 1248
OFFSET
0,2
COMMENTS
This is an approximation to A004922 (floor of n*phi^7, where phi is the golden ratio, A001622).
The "+ 0^n - 0^(n mod 29)" corrects a(n), for n=0 and multiples of 29. (See examples below.)
LINKS
Eric Weisstein's World of Mathematics, Golden Ratio
Wikipedia, Golden ratio
EXAMPLE
For n = 0, 29*n + floor(0.0) + 0^0 - 0^(0) = 0 + 0 + 1 - 1 = 0 (n=29*0).
For n = 28, 29*n + floor(0.97) + 0^28 - 0^(28)= 812 + 0 + 0 - 0 = 812.
For n = 29, 29*n + floor(1.0) + 0^29 - 0^(0) = 841 + 1 + 0 - 1 = 841 (n=29*1).
For n = 31, 29*n + floor(1.1) + 0^31 - 0^(2) = 899 + 1 + 0 - 0 = 900.
For n = 87, 29*n + floor(3.0) + 0^87 - 0^(0) = 2523 + 3 + 0 - 1 = 2525 (n=29*3).
PROG
(Python)
from math import *
from decimal import *
getcontext().prec = 100
for n in range(0, 101):
..print n, (29*n+floor(n/29.0))+ 0**n-0**(n%29)
(Python)
def A248786(n):
a, b = divmod(n, 29)
return 29*n+a-int(not b) if n else 0 # Chai Wah Wu, Jul 27 2022
(Magma) [(29*n+Floor(n/29))+ 0^n-0^(n mod 29): n in [0..60]]; // Vincenzo Librandi, Oct 14 2014
(PARI) a(n) = 29*n+ n\29 + 0^n - 0^(n % 29); \\ Michel Marcus, Oct 14 2014
CROSSREFS
Cf. A001622 (phi), A195819 (29*n).
Cf. A004922 (floor(n*phi^7)), A004962 (ceiling(n*phi^7)), A004942 (round(n*phi^7)).
Sequence in context: A164011 A048846 A195819 * A004922 A249079 A004942
KEYWORD
nonn,easy
AUTHOR
Karl V. Keller, Jr., Oct 14 2014
STATUS
approved