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A045572
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Numbers that are odd but not divisible by 5.
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40
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1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 93, 97, 99, 101, 103, 107, 109, 111, 113, 117, 119, 121, 123, 127, 129, 131, 133, 137, 139, 141, 143, 147, 149, 151, 153
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OFFSET
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1,2
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COMMENTS
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Contains the repunits R_n, (A000042 or A002275): For any m in the sequence (divisible by neither 2 nor 5), Euler's theorem (i.e. m|10^m-1=9*R_n) guarantees that R_n is always some multiple of m (see A099679) and thus forms a subsequence. - Lekraj Beedassy, Oct 26 2004
Inverse formula: n = 4*floor(a(n)/10) + floor([a(n) mod 10]/3) + 1 - Carl R. White, Feb 06 2008
Numbers ending with 1, 3, 7 or 9. [From Lekraj Beedassy , Apr 04 2009]
A000035(a(n))*(1-A079998(a(n)))=1; complement of A065502. [From Reinhard Zumkeller, Nov 15 2009]
Union of evenish and oddish numbers, cf. A045797, A045798. [Reinhard Zumkeller, Dec 10 2011]
Numbers k such that k^(4*j) mod 10 = 1, for any j. [From Gary Detlefs, Jan 03 2012]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
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a(n)=-1+Sum_{k=0..n}{(1/12)*{5*(k mod 4)+11*[(k+1) mod 4]-[(k+2) mod 4]+5*[(k+3) mod 4]}} - Paolo P. Lava, Dec 20 2007
a(n) = 10*floor((n-1)/4) + 2*floor( (4*[(n-1) mod 4]+1)/3 ) + 1 a(n) = a(n-1) + 2 + 2*floor([(x+6) mod 10]/9) - Carl R. White , Feb 06 2008
a(n) = 2*n + 2*floor((n-3)/4) + 1 - Kenneth Hammond (weregoose(AT)gmail.com), Mar 07 2008
a(n) = -1 + 2*n + 2*floor((n+1)/4) - Kenneth Hammond (weregoose(AT)gmail.com), Mar 25 2008
a(n)= a(n-1) +a(n-4) -a(n-5). G.f.: x*(1+2*x+4*x^2+2*x^3+x^4)/ ((1+x) * (x^2+1) * (x-1)^2). - R. J. Mathar, Sep 22 2009
a(n) = (10*n+2*(-1)^(n*(n+1)/2)-(-1)^n-5)/4. - Bruno Berselli, Nov 06 2011
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EXAMPLE
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a(18) = 10*floor(17/4) + 2*floor( (4*[17 mod 4]+1)/3 ) + 1
= 10*4 + 2*floor( (4*[1]+1)/3 ) + 1
= 40 + 2*floor(5/3) + 1
= 40 + 2*1 + 1
= 43
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MATHEMATICA
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Flatten[Table[10n + {1, 3, 7, 9}, {n, 0, 19}]] (* Alonso del Arte, Jan 13 2012 *)
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PROG
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(GNU bc) scale=0; for(n=1; n<=100; n++) 10*((n-1)/4)+2*((4*((n-1)%4)+1)/3)+1 /* Carl R. White, Feb 06 2008 */
(PARI) a(n)=10*(n>>2)+[-1, 1, 3, 7][n%4+1] \\ Charles R Greathouse IV, Jul 31 2011
(MAGMA) [ 2*n + 2*Floor((n-3)/4) + 1: n in [1..70] ]; // Vincenzo Librandi, Aug 01 2011
(Haskell)
a045572 n = a045572_list !! (n-1)
a045572_list = filter ((/= 0) . (`mod` 5)) a005408_list
-- Reinhard Zumkeller, Dec 10 2011
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CROSSREFS
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See also A085820, A082768 (Numbers that begin with 1, 3, 7 or 9).
Cf. A005408.
Sequence in context: A165631 A005818 A085820 * A069254 A105585 A080903
Adjacent sequences: A045569 A045570 A045571 * A045573 A045574 A045575
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Jeff Burch
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STATUS
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approved
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