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3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191
(list;
graph;
refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 12 ).
Binary expansion ends 11.
These the numbers for which zeta(2*x+1) needs just 2 terms to be evaluated. - Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 16 2004 [This comment needs clarification]
a(n) = smallest k such that for every r from 0 to 2n-1 there exist j and i, k >= j > i > 2n-1, such that j - i == r ( mod (2n-1)), with (k,(2n-1))=(j,(2n-1))=(i,(2n-1)) = 1. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 24 2003
Any (4n+3)-dimensional manifold endowed with a mixed 3-Sasakian structure is an Einstein space with Einstein constant lambda = 4n+2 [Theorem 3, p.10 of Ianus et al]. [Jonathan Vos Post, Nov 24 2008]
Solutions to the equation x^(2*x)=3*x (mod 4*x). [From F. Firoozbakht, May 02 2010]
a(n) = A017137(n)/2. [From Reinhard Zumkeller, Jul 13 2010]
For all n, a(n) is not a^2+b^2. [Vincenzo Librandi, Nov 20 2010]
First differences of A084849. [Reinhard Zumkeller, Apr 02 2011]
Numbers n such that {1,2,3, ..., n} is a losing position in the game of Nim. - Franklin T. Adams-Watters, Jul 16 2011
Numbers n such that there are no primes p that satisfy the relationship p XOR n = p + n. - Brad Clardy, Jul 22 2012
The XOR of all numbers from 1 to a(n) is 0. - David W. Wilson, Apr 21 2013
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LINKS
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Table of n, a(n) for n=0..47.
Guo-Niu Han, Enumeration of Standard Puzzles
Stere Ianus, Mihai Visinescu and Gabriel-Eduard Vilcu, Hidden symmetries and Killing tensors on curved spaces, Nov 21, 2008. [From Jonathan Vos Post, Nov 24 2008]
Tanya Khovanova, Recursive Sequences
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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G.f.: (3+x)/(1-x)^2 - Paul Barry, Feb 27 2003
Complement of A004773. - Reinhard Zumkeller, Aug 29 2005
a(n)=2*a(n-1)-a(n-2); a(0)=3, a(1)=7. [From Philippe DELEHAM, Nov 03 2008]
a(n)=8*n-a(n-1)+2 (with a(0)=3) [From Vincenzo Librandi, Nov 20 2010]
a(n) = A005408(A005408(n)). [Reinhard Zumkeller, Jun 27 2011]
a(n) = 3 + A008586(n). - Omar E. Pol, Jul 27 2012
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MAPLE
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seq( 3+4*n, n=0..100 );
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MATHEMATICA
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Range[3, 500, 4] (* From Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
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PROG
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(Haskell)
a004767 = (+ 3) . (* 4)
a004767_list = [3, 7 ..] -- Reinhard Zumkeller, Oct 03 2012
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CROSSREFS
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Cf. A008586, A016813, A016825.
Sequence in context: A103543 A172338 A189787 * A131098 A118894 A194397
Adjacent sequences: A004764 A004765 A004766 * A004768 A004769 A004770
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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