The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A068515 A measure of how close the square root of 2 is to rational numbers. 0
 2, -12, 12, -12, 70, 12, -70, 26, -33, 70, -25, -408, 34, -70, 70, -43, 408, 39, -146, 70, -70, 195, -49, -408, 70, -113, 147, -70, 2378, 70, -195, 126, -100, 408, 70, -408, 114, -146, 253, -93, -2378, 106, -228, 195, -125, 855, 100, -408, 165, -173, 408, -113, -1135, 147, -252, 286, -146, 2378, 135, -408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS New peaks (in absolute terms) occur when n is a Pell number (1,2,5,12,29,70,... A000129) and take alternate Pell values with alternating signs (2,-12,70,-408,2378,-13860,... A001542). Each new peak (after the first) appears twice (with different signs) before the next peak, when n is a numerator of a continued fraction convergent to sqrt(2) (3,7,17,41,99,... A001333) and when n is twice a Pell number (4,10,24,58,140,... A052542). LINKS FORMULA a(n) =round[1/(sqrt(2)-round[sqrt(2)*n]/n)] =round[1/(sqrt(2)-A022846(n)/n)] where sqrt(2)=1.41421356... EXAMPLE a(5) = round[1/(sqrt(2)-round[sqrt(2)*5]/5)] = round[1/(sqrt(2)-7/5)] = round[70.355] = 70, i.e. sqrt(2) is about 1/70 more than the nearest multiple of 1/5. CROSSREFS Cf. A066212. Sequence in context: A216478 A181060 A171446 * A088240 A168457 A045895 Adjacent sequences:  A068512 A068513 A068514 * A068516 A068517 A068518 KEYWORD sign AUTHOR Henry Bottomley, Mar 19 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 16:20 EST 2020. Contains 338906 sequences. (Running on oeis4.)