1,2

A000129(n+1) = A079496(n) + a(n), where A079496 = (1, 3, 5, 17, 29, 99,...). Example: A000129(5) = 29 = A079496(4) + a(4) = 17 + 12. - Gary W. Adamson (qntmpkt(AT)yahoo.ciom), Sep 18 2007

Apart from the first two terms (1, 2) the sequence gives the numbers k which are perfect medians. Namely: if k is even -> sum_{j=2, 4, 6, .., k-2} {j} = sum_{j=k+2, k+4, k+6,..k+m} {j} (for some m even); if k is odd -> sum_{j=1, 3, 5, .., k-2} {j} = sum_{j=k+2, k+4, k+6,..k+m} {j} (for some m even). See also A001109. - Paolo P. Lava (ppl(AT)spl.at), Jan 28 2008

The upper principal and intermediate convergents to 2^(1/2), beginning with 2/1, 3/2, 10/7, 17/12, 58/41, form a strictly decreasing sequence; essentially, numerators=A143609 and denominators=A084068. - Clark Kimberling (ck6(AT)evansville.edu), Aug 27 2008

Clark Kimberling, "Best lower and upper approximates to irrational numbers," Elemente der Mathematik, 52 (1997) 122-126.

Serge Lang, Introduction to Diophantine Approximations, Addison-Wesley, New York, 1966.

"A Diofloortin equation" : n such that 2*n^2=floor(n*sqrt(2)*ceil(n*sqrt(2))).

a(n)a(n+3) = -2 + a(n+1)a(n+2).

G.f.: x(1+x)^2/(1-6x^2+x^4); a(n)=((sqrt(2)+1)^n-(sqrt(2)-1)^n)((sqrt(2)/8-1/4)*(-1)^n+sqrt(2)/8+1/4); a(n+1)=sum{k=0..floor((n+1)/2), 2^k*(C(n+1,2k)-C(n,2k+1)*(1-(-1)^n)/2}; - Paul Barry (pbarry(AT)wit.ie), Jun 06 2006

Equals A133566 * A000129, where A000129 = the Pell sequence. - Gary W. Adamson (qntmpkt(AT)yahoo.ciom), Sep 18 2007

Cf. A084069, A084070.

Bisections are A001542 and A002315.

Cf. A133566, A079496.

Sequence in context: A073710 A092831 A055257 this_sequence A046243 A103886 A130710

Adjacent sequences: A084065 A084066 A084067 this_sequence A084069 A084070 A084071

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003