cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A071080 Determinant of the n X n matrix whose element (i,j) equals the |i-j|-th composite number, or 1 if i=j.

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%I A071080 #18 Dec 03 2024 03:27:10
%S A071080 1,-15,125,-935,6096,-38340,240864,-1497584,8611328,-49201152,
%T A071080 277473280,-1541996288,7852493824,-39972516864,195624648704,
%U A071080 -789661486080,3052709008384,-9659706075392,30089357409792,-63825905935360,63965499203712,-8296932715920,-1139418909751008
%N A071080 Determinant of the n X n matrix whose element (i,j) equals the |i-j|-th composite number, or 1 if i=j.
%H A071080 Robert Israel, <a href="/A071080/b071080.txt">Table of n, a(n) for n = 1..1000</a>
%p A071080 comps:= remove(isprime,[$4 .. 1000]):
%p A071080 f:= proc(n) local M;
%p A071080   M:= Matrix(n,n,(i,j) -> `if`(i=j,1,comps[abs(i-j)]));
%p A071080   LinearAlgebra:-Determinant(M)
%p A071080 end proc:
%p A071080 map(f, [$1..25]); # _Robert Israel_, Dec 03 2024
%t A071080 Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; f[n_] := Det[ Table[ If[i == j, 1, Composite[ Abs[i - j]]], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 20}]
%Y A071080 Cf. A071078, A071079, A071081, A071082, A071083.
%Y A071080 Cf. A374069 (permanent).
%K A071080 sign
%O A071080 1,2
%A A071080 _Robert G. Wilson v_, May 26 2002
%E A071080 a(21)-a(23) from _Stefano Spezia_, Jun 27 2024