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 A157927 Joint-rank array of the numbers i^2+j^2, where i>=0, j>=0. 1
 1, 2, 2, 4, 3, 4, 7, 5, 5, 7, 10, 8, 6, 8, 10, 14, 11, 9, 9, 11, 14, 19, 15, 13, 12, 13, 15, 19, 24, 20, 16, 14, 14, 16, 20, 24, 30, 25, 21, 18, 17, 18, 21, 25, 30, 37, 31, 27, 23, 22, 22, 23, 27, 31, 37, 44, 38, 32, 28, 26, 25, 26, 28, 32, 38, 44 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The definition of joint-rank array given at A182801 is here extended to arrays R={f(i,j)} for which the numbers f(i,j) are not necessarily distinct.  Specifically, all duplicates are assigned the same rank when all the numbers in R are jointly ranked.  Let {a(i,j)} denote the resulting joint-rank array.  In case all f(i,j) are positive integers, a(i,j)=f(i,j)-L(i,j), where L(i,j) is the number of numbers in R that are <=f(i,j). (Row 1)=A047808. LINKS EXAMPLE A corner of the array R={i^2+j^2} is 0....1....4....9...16... 1....2....5...10...17... 4....5....8...13...20... 9...10...13...18...25... Replace each term of R by its rank: 1....2....4....7...10... 2....3....5....8...11... 4....5....6....9...13... 7....8....9...12...14... CROSSREFS Cf. A182801, A048147. Sequence in context: A205793 A178431 A233574 * A227256 A328774 A131816 Adjacent sequences:  A157924 A157925 A157926 * A157928 A157929 A157930 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 17 2010 STATUS approved

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Last modified September 22 22:13 EDT 2021. Contains 347608 sequences. (Running on oeis4.)