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 A038122 Start with {1,2,...,n}, replace any two numbers a,b with |a^2-b^2|, repeat until single number k remains; a(n) = minimal value of k. 0
 1, 3, 0, 16, 15, 63, 8, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0, 3, 1, 0, 0, 1, 3, 0, 4, 3, 3, 4, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Due mostly to the efforts of Dean Hickerson, supported by David W. Wilson and Michael Kleber, it is now known that this has period 12 beginning at n=8. LINKS Dean Hickerson and Michael Kleber, Reducing a Set by Subtracting Squares, J. Integer Sequences, Vol. 2, 1999, #4. Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,-1,0,0,1). FORMULA For n<4 and n>7, a(n) = n*(n+1)/2 mod 6 = A010875(A000217(n)). - Henry Bottomley, Feb 24 2003 a(n) = a(n-3)-a(n-6)+a(n-9) for n>16. - Colin Barker, Oct 01 2014 G.f.: x*(4*x^15 +60*x^14 +12*x^13 +8*x^12 -60*x^11 -12*x^10 -8*x^9 +60*x^8 +12*x^7 +7*x^6 -63*x^5 -12*x^4 -15*x^3 -3*x -1) / ((x -1)*(x^2 +1)*(x^2 +x +1)*(x^4 -x^2 +1)). - Colin Barker, Oct 01 2014 EXAMPLE a(2) = 3 from (1,2); a(3) = 0 from ((1,2),3); a(4) = 16 from (((1,2),3),4); a(5) = 15 from ((((2,3),5),1),4) a(6) = 63 from (((1,4),(3,5)),(2,6)) [ Michael Kleber ] a(7) = 8 from (((((4,5),6),(2,7)),1),3) [ Kleber ] a(8) = 0 from ((((4,5),7)(2,6))((1,3),8)) [ Guy ] a(9) = 3 from (2,(1,(((6,7),((3,4),8)),(5,9)))) [ Kleber ] a(10)= 1 from ((((((((4,5),9),6),(8,10)),2),3),7),1) [ This and the following are due to Dean Hickerson ] a(11)= 0 from ((((((3,7),(9,11)),6),(8,10)),(1,2)),(4,5)) a(12)= 0 from ((((((1,3),7),(8,10)),(((5,6),9),(11,12))),2),4) a(13)= 1 from (((((((((3,7),(9,11)),6),(8,10)),5),(12,13)),2),4),1) ... MATHEMATICA LinearRecurrence[{0, 0, 1, 0, 0, -1, 0, 0, 1}, {1, 3, 0, 16, 15, 63, 8, 0, 3, 1, 0, 0, 1, 3, 0, 4}, 120] (* Harvey P. Dale, Jul 29 2015 *) PROG (PARI) a(n)=if(n<4||n>7, n*(n+1)/2%6, [16, 15, 63, 8][n-3]) \\ Charles R Greathouse IV, Feb 10 2017 CROSSREFS Sequence in context: A013407 A013494 A290580 * A143779 A240244 A036968 Adjacent sequences:  A038119 A038120 A038121 * A038123 A038124 A038125 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)