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 A071797 Restart counting after each new odd integer (a fractal sequence). 17
 1, 1, 2, 3, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446. This is also a triangle read by rows in which row n lists the first 2*n-1 positive integers, n >= 1 (see example). - Omar E. Pol, May 29 2012 A071797(n) mod 2 = A071028(n). - Boris Putievskiy, Jul 24 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, Daisy Ann A. Disu, On Fractal Sequences, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 109-113. C. Kimberling, Numeration systems and fractal sequences, Acta Arithmetica 73 (1995) 103-117. F. Smarandache, Only Problems, Not Solutions!, Phoenix,AZ: Xiquan,1993. FORMULA a(n) = 1 + A053186(n-1). a(n) = n-1-ceiling(sqrt(n))*(ceiling(sqrt(n))-2); n>0. a(n) = n-floor(sqrt(n-1))^2, distance between n and the next smaller square. - Marc LeBrun, Jan 14 2004 EXAMPLE a(1)=1; a(9)= 5; a(10)=1; From Omar E. Pol, May 29 2012: (Start) Written as a triangle the sequence begins: 1; 1, 2, 3; 1, 2, 3, 4, 5; 1, 2, 3, 4, 5, 6, 7; 1, 2, 3, 4, 5, 6, 7, 8, 9; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15; Row n has length 2*n - 1 = A005408(n-1). (End) MAPLE A071797 := proc(n)     n-A048760(n-1) ; end proc: # R. J. Mathar, May 29 2016 MATHEMATICA Array[Range[2# - 1]&, 10] // Flatten (* Jean-François Alcover, Jan 30 2018 *) PROG (PARI) a(n)=if(n<1, 0, n-sqrtint(n-1)^2) (Haskell) import Data.List (inits) a071797 n = a071797_list !! (n-1) a071797_list = f \$ tail \$ inits [1..] where    f (xs:_:xss) = xs ++ f xss -- Reinhard Zumkeller, Apr 14 2014 CROSSREFS Cf. A002260, A004737, A006590, A027052, A071028, A071797, A078358, A078446. Cf. A074294. Sequence in context: A274641 A003315 A194107 * A025481 A124171 A276146 Adjacent sequences:  A071794 A071795 A071796 * A071798 A071799 A071800 KEYWORD easy,nonn,tabf AUTHOR Antonio Esposito (antonio.b.esposito(AT)italtel.it), Jun 06 2002 STATUS approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)