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 A054431 Array read by antidiagonals: T(x, y) tells whether (x, y) are coprime (1) or not (0). 17
 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Array is read along (x, y) = (1, 1), (1, 2), (2, 1), (1, 3), (2, 2), (3, 1), ... There are nontrivial infinite paths of 1's in this sequence, moving only 1 step down or to the right at each step. Starting at (1,1), move down to (2,1), then (3,1), ..., (13,1). Then move right to (13,2), (13,3), ..., (13,11). From this point, alternate moving down to the next prime row, and right to the next prime column. - Franklin T. Adams-Watters, May 27 2014 LINKS FORMULA T(n, k) = T(n, k-n) + T(n-k, k) starting with T(n, k)=0 if n or k are nonpositive and T(1, 1)=1. T(n, k) = A054521(n, k) if n>=k, = A054521(k, n) if n<=k. Antidiagonal sums are phi(n) = A000010(n). - Henry Bottomley, May 14 2002 As a triangular array for n>=1, 1<=k<=n, T(n,k) = |K(n-k+1|k)| where K(i|j) is the Kronecker symbol. - Peter Luschny, Aug 05 2012 Dirichlet g.f.: Sum_{n>=1} Sum_{k>=1} [gcd(n,k)=1]/n^s/k^c = zeta(s)*zeta(c)/zeta(s + c). - Mats Granvik, May 19 2021 EXAMPLE Rows start:   1, 1, 1, 1, 1, 1, ...;   1, 0, 1, 0, 1, 0, ...;   1, 1, 0, 1, 1, 0, ...;   1, 0, 1, 0, 1, 0, ...;   1, 1, 1, 1, 0, 1, ...;   1, 0, 0, 0, 1, 0, ...; MAPLE reduced_residue_set_0_1_array := n -> one_or_zero(igcd(((n-((trinv(n)*(trinv(n)-1))/2))+1), ((((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1) )); one_or_zero := n -> `if`((1 = n), (1), (0)); # trinv given at A054425 A054431_row := n -> seq(abs(numtheory[jacobi](n-k+1, k)), k=1..n); for n from 1 to 14 do A054431_row(n) od; # Peter Luschny, Aug 05 2012 MATHEMATICA t[n_, k_] := Boole[CoprimeQ[n, k]]; Table[t[n-k+1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 21 2012 *) PROG (Sage) def A054431_row(n): return [abs(kronecker_symbol(n-k+1, k)) for k in (1..n)] for n in (1..14): print(A054431_row(n)) # Peter Luschny, Aug 05 2012 CROSSREFS Equal to A003989 with non-one values replaced with zeros. Cf. A047999, A054432, A055088, A054521, A215200. Sequence in context: A166282 A047999 A323378 * A164381 A106470 A106465 Adjacent sequences:  A054428 A054429 A054430 * A054432 A054433 A054434 KEYWORD nonn,tabl AUTHOR STATUS approved

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Last modified June 30 14:51 EDT 2022. Contains 354943 sequences. (Running on oeis4.)