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A042965
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Numbers not congruent to 2 mod 4.
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30
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0, 1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 92
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence (starting at 3) gives values of AUB, sorted and duplicates removed. Values of AUBUC give same sequence - David W. Wilson (davidwwilson(AT)comcast.net)
These are the nonnegative integers that can be written as a difference of two squares i.e. n=x^2-y^2 for integers x,y. - Sharon Sela (sharonsela(AT)hotmail.com), Jan 25 2002
Also numbers n such that Kronecker(4,n)==mu(gcd(4,n)). - Jon Perry (perry(AT)globalnet.co.uk), Sep 17 2002
Count, sieving out numbers of the form 2(2n+1) (A016825, "nombres pair-impairs"). A generalized Chebyshev transform of the Jacobsthal numbers: apply the transform g(x)->(1/(1+x^2))g(x/(1+x^2)) to the g.f. of A001045(n+2). Partial sums of 1,2,1,1,2,1,..... - Paul Barry (pbarry(AT)wit.ie), Apr 26 2005
For n>1, equals union of A020883 and A020884. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 28 2004
The sequence 1,1,3,4,5,... is the image of A001045(n+1) under the mapping g(x)->g(x/(1+x^2)). - Paul Barry (pbarry(AT)wit..ie), Jan 16 2005
With offset 0 starting (1, 3, 4,...) = INVERT transform of A009531 starting (1, 2, -1, -4, 1, 6,...) with offset 0.
Apparently these are the regular numbers modulo 4 [Haukkanan & Toth].- R. J. Mathar, Oct 07 2011
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
P. Haukkanen, L. Toth, An analogue of Ramanujan's sum with respect to regular integers (mod r), Ramanjuan J. (to appear, 2011)
Ron Knott, Pythagorean Triples and Online Calculators
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,0,1,-1)
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FORMULA
| a(n) = +1*a(n-1) +1*a(n-3) -1*a(n-4).
Partial sums of the period-3 sequence 0, 1, 1, 2, 1, 1, 2, 1, 1, 2, ... (A101825). - Ralf Stephan.
G.f.: x^2*(1+x)^2/((1-x)^2*(1+x+x^2)); a(n)=sum{k=0..floor(n/2), binomial(n-k-1, k)*A001045(n-2*k)}, n>0. - Paul Barry (pbarry(AT)wit..ie), Jan 16 2005, R. J. Mathar, Dec 09 2009
a(n)=floor((4*n-1)/3). [From Gary Detlefs (gdetlefs(AT)aol.com), May 14 2011]
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MATHEMATICA
| nn=100; Complement[Range[0, nn], Range[2, nn, 4]] (* From Harvey P. Dale, May 21 2011 *)
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PROG
| (PARI) a(n)=(4*n-1)\3 \\ Charles R Greathouse IV, Jul 25 2011
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CROSSREFS
| Cf. A047209, A020883, A020884, A009531.
Sequence in context: A183147 A074227 A122906 * A005848 A187885 A039065
Adjacent sequences: A042962 A042963 A042964 * A042966 A042967 A042968
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Peter Pein and Ralf Stephan, Jun 17 2007
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