Search: id:A144396
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%I A144396
%S A144396 3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,
%T A144396 53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,
%U A144396 99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133
%N A144396 The odd numbers greater than 1.
%C A144396 Last number of the n-th row of the triangle described in A142717.
%C A144396 If negated, these are also the values at local minima of the sequence 
               A141620.
%C A144396 a(n)=sqrt(8n+1) when n is a triangular number (1, 3, 6, etc) [A000217] 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 11 2009]
%F A144396 Except for the first term of [A002378], if X=[A144396], Y=[A007395], 
               A= [A002378], we have, for all other terms, Pell's equation: [A144396]^2 
               - [A002378]*[A007395]^2=1; (X^2-A*Y^2=1); example: 3^2-2*2^2=1; 5^2-6*2^2=1; 
               19^2-90*2^2=1, and so on. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 11 2009]
%F A144396 a(n)=A005408(n+1)=A000290(n+1)-A000290(n).
%F A144396 G.f.: x*(3-x)/(1-x)^2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Aug 30 2009]
%Y A144396 Cf. A000217 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 
               11 2009]
%Y A144396 Cf. A002378, A007395 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 11 2009]
%Y A144396 Sequence in context: A157142 A004273 A005408 this_sequence A060747 A089684 
               A105356
%Y A144396 Adjacent sequences: A144393 A144394 A144395 this_sequence A144397 A144398 
               A144399
%K A144396 nonn,less,easy
%O A144396 1,1
%A A144396 Paul Curtz (bpcrtz(AT)free.fr), Oct 03 2008
%E A144396 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 21 2009
%E A144396 More terms from Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 27 
               2009

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