%I A038722
%S A038722 1,3,2,6,5,4,10,9,8,7,15,14,13,12,11,21,20,19,18,17,16,28,27,26,25,
%T A038722 24,23,22,36,35,34,33,32,31,30,29,45,44,43,42,41,40,39,38,37,55,54,
%U A038722 53,52,51,50,49,48,47,46,66,65,64,63,62,61,60,59,58,57,56,78,77,76
%N A038722 Take the sequence of natural numbers (A000027) and reverse successive 
               subsequences of lengths 1,2,3,4,...
%C A038722 The rectangular array having A038722 as antidiagonals is the transpose 
               of the rectangular array given by A000217. Column 1 of array A038722 
               is A000124 (central polygonal numbers). Array A038722 is the dispersion 
               of the complement of A000124. - Clark Kimberling (ck6(AT)evansville.edu), 
               Apr 05 2003
%C A038722 a(n) is the smallest number not yet in the sequence such that n + a(n) 
               is one more than a square. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Apr 06 2009]
%D A038722 Suggested by correspondence with Michael Somos.
%D A038722 R. Honsberger, "Ingenuity in Mathematics", Table 10.4 on page 87.
%H A038722 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A038722 a(n) =[sqrt(2n-1)-1/2]*[sqrt(2n-1)+3/2]-n+2 =A061579(n-1)+1. Seen as 
               a square table by antidiagonals, T(n, k)=k+(n+k-1)*(n+k-2)/2, i.e. 
               the transpose of A000027 as a square table.
%F A038722 G.f.: g(x)=x/(1-x)*(psi(x)-x/(1-x)+2*sum{k>=0, k*x^(k*(k+1)/2)}) where 
               psi(x)=sum{k>=0, x^(k*(k+1)/2)}=1/2*x^(-1/8)*theta_2(0,x^(1/2) is 
               a Ramanujan theta function. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Aug 08 2007
%Y A038722 A self-inverse permutation of the natural numbers.
%Y A038722 Cf. A000027, A020703.
%Y A038722 Sequence in context: A058401 A105027 A120913 this_sequence A145522 A131968 
               A132665
%Y A038722 Adjacent sequences: A038719 A038720 A038721 this_sequence A038723 A038724 
               A038725
%K A038722 nonn,tabl
%O A038722 1,2
%A A038722 N. J. A. Sloane (njas(AT)research.att.com), May 02 2000