A004776 Numbers not congruent to 5 (mod 8).
0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78
Offset: 1
Links
- Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
Programs
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Haskell
a004776 n = a004776_list !! (n-1) a004776_list = filter ((/= 5) . (`mod` 8)) [0..] -- Reinhard Zumkeller, Aug 17 2012
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Magma
[n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 4, 6, 7]]; // Wesley Ivan Hurt, Jul 22 2016
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Maple
A004776:=n->8*floor(n/7)+[0, 1, 2, 3, 4, 6, 7][(n mod 7)+1]: seq(A004776(n), n=0..100); # Wesley Ivan Hurt, Jul 22 2016
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Mathematica
DeleteCases[Range[0,80],?(Mod[#,8]==5&)] (* _Harvey P. Dale, Apr 28 2014 *)
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PARI
is(n)=n%8!=5 \\ Charles R Greathouse IV, Mar 07 2013
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PARI
A004776(n)=n+(n-6)\7 \\ M. F. Hasler, Nov 02 2013
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Python
def A004776(n): return n-1+(n+1)//7 # Chai Wah Wu, Feb 24 2025
Formula
Numbers that are congruent to {0, 1, 2, 3, 4, 6, 7} mod 8.
G.f.: x^2*(1+x+x^2+x^3+2*x^4+x^5+x^6) / ((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2). - R. J. Mathar, Oct 25 2011
a(n) = n + floor((n-6)/7). - M. F. Hasler, Nov 02 2013
From Wesley Ivan Hurt, Jul 22 2016: (Start)
a(n) = a(n-1) + a(n-7) - a(n-8) for n>8; a(n) = a(n-7) + 8 for n>7.
a(n) = (56*n - 63 + (n mod 7) - 6*((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) + ((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.
a(7k) = 8k-1, a(7k-1) = 8k-2, a(7k-2) = 8k-4, a(7k-3) = 8k-5, a(7k-4) = 8k-6, a(7k-5) = 8k-7, a(7k-6) = 8k-8. (End)
Extensions
Edited by M. F. Hasler, Nov 02 2013
Comments