The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083037 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A083037

a(n)=2*A083036(n)-n. Also -A123737(n).
(history; published version)

#10 by Alois P. Heinz at Thu Feb 07 17:15:01 EST 2013

STATUS

reviewed

approved

#9 by Joerg Arndt at Thu Feb 07 14:13:18 EST 2013

STATUS

proposed

reviewed

#8 by Charles R Greathouse IV at Thu Feb 07 14:08:34 EST 2013

STATUS

editing

proposed

#7 by Charles R Greathouse IV at Thu Feb 07 14:08:31 EST 2013

LINKS

Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, <a href="http://www.math.uiuc.edu/~reznick/ors.pdf">Almost alternating sums</a>, Amer. Math. Monthly, Vol. 113 (October 2006), pp. 673-688.

FORMULA

O'Bryant, Reznick, & Serbinowska show that |a(n)| <= k log n + 1, with k = 1/(2 log (1 + sqrt(2))), and further a(n) > k log n + 0.78 infinitely often. - Charles R Greathouse IV, Feb 07 2013

PROG

(PARI) a(n)=-sum(i=1, n, (-1)^sqrtint(2*i^2)) \\ Charles R Greathouse IV, Feb 07 2013

STATUS

approved

editing

#6 by Russ Cox at Fri Mar 30 18:39:18 EDT 2012

AUTHOR

_Benoit Cloitre (benoit7848c(AT)orange.fr), _, Apr 17 2003

Discussion

Fri Mar 30

18:39

OEIS Server: https://oeis.org/edit/global/216

#5 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

KEYWORD

sign,new

sign

AUTHOR

Benoit Cloitre (abmtbenoit7848c(AT)wanadooorange.fr), Apr 17 2003

#4 by N. J. A. Sloane at Wed Dec 06 03:00:00 EST 2006

NAME

a(n)=2*A083036(n)-n. Also -A123737(n).

CROSSREFS

Cf. A083035, A083036, A083038, A123737.

KEYWORD

sign,new

sign

#3 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

KEYWORD

sign,new

sign

AUTHOR

Benoit Cloitre (abcloitreabmt(AT)modulonetwanadoo.fr), Apr 17 2003

#2 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

KEYWORD

sign,new

sign

AUTHOR

Benoit Cloitre (abcloitre(AT)wanadoomodulonet.fr), Apr 17 2003

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

a(n)=2*A083036(n)-n.

DATA

1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 0, -1, 0, -1, -2, -1, 0

OFFSET

1,8

CROSSREFS

Cf. A083035, A083036, A083038.

KEYWORD

sign

AUTHOR

Benoit Cloitre (abcloitre(AT)wanadoo.fr), Apr 17 2003

STATUS

approved