1,3

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

Ron Knott, Pythagorean Triples and Online Calculators

Partial sums of the period-3 sequence 0, 1, 1, 2, 1, 1, 2, 1, 1, 2, ... (A101825) with g.f. x*(1+x)^2/(1-x^3). - Ralf Stephan.

G.f. (follows from previous formula line): x(1+x)^2/(1-x-x^3+x^4); a(n)=sum{k=0..floor(n/2), binomial(n-k-1, k)A001045(n-2k)}, n>0. - Paul Barry (pbarry(AT)wit..ie), Jan 16 2005

(PARI) for (x=1, 200, for (y=1, 200, if (kronecker(x, y)==moebius(gcd(x, y)), write("km.txt", x, "; ", y, " : ", kronecker(x, y)))))

Cf. A047209, A020883 and A020884.

Sequence in context: A137905 A074227 A122906 this_sequence A005848 A039065 A139711

Adjacent sequences: A042962 A042963 A042964 this_sequence A042966 A042967 A042968

nonn,nice

njas

Edited by njas at the suggestion of Andrew Plewe, Peter Pein and Ralf Stephan, Jun 17 2007