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 A020703 Take the sequence of natural numbers (A000027) and reverse successive subsequences of lengths 1,3,5,7,... 10
 1, 4, 3, 2, 9, 8, 7, 6, 5, 16, 15, 14, 13, 12, 11, 10, 25, 24, 23, 22, 21, 20, 19, 18, 17, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 81, 80, 79, 78, 77 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Arrange A000027, the natural numbers, into a (square) spiral, say clockwise as shown in A068225. Read the numbers from the resulting counterclockwise spiral of the same shape that also begins with 1 and this sequence results. - Rick L. Shepherd, Aug 04 2006 Contribution from Hieronymus Fischer, Apr 30 2012: (Start) The sequence may also be defined as follows: a(1)=1, a(n)=m^2 (where m^2 is the least square > a(k) for 1<=k 0 is not in the set {a(k)| 1<=k=0. a(n+1)=(sqrt(a(n)-1)+2)^2, if a(n)-1 is a square, a(n+1)=a(n)-1, else. a(n)=2*(floor(sqrt(n-1))+1)*floor(sqrt(n-1))-n+2. (End) EXAMPLE a(2)=4=2^2, since 2^2 is the least square >2=a(1) and the minimal number not yet in the sequence is 2>1=a(1); a(8)=6=a(7)-1, since the minimal number not yet in the sequence (=5) is <=7=a(7). MATHEMATICA Flatten[Table[Range[n^2, (n-1)^2+1, -1], {n, 10}]] (* Harvey P. Dale, Jan 10 2016 *) With[{nn=20}, Flatten[Reverse/@TakeList[Range[nn^2], Range[1, nn, 2]]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jan 28 2019 *) PROG (PARI) a(n)=local(t); if(n<1, 0, t=sqrtint(n-1); 2*(t^2+t+1)-n) CROSSREFS A self-inverse permutation of the natural numbers. Cf. A000027, A038722. Cf. A132666, A132664, A132665, A132674. Sequence in context: A021235 A273991 A292828 * A084483 A266150 A276612 Adjacent sequences:  A020700 A020701 A020702 * A020704 A020705 A020706 KEYWORD nonn AUTHOR N. J. A. Sloane, May 02 2000 STATUS approved

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Last modified March 31 20:55 EDT 2020. Contains 333151 sequences. (Running on oeis4.)