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%I #10 Oct 25 2023 08:47:32
%S 1,2,4,2,5,3,2,4,2,13,3,2,4,2,5,11,2,4,2,37,3,2,4,2,61,3,2,4,2,97,3,2,
%T 4,2,151,3,2,229,3,2,4,2,349,3,2,4,2,23,47,2,5,227,2,4,2,5,11,2,4,2,
%U 17,83,2,4,2,751,3,2,1129,3,2,4,2,1699,3,2,2551,3,2,7
%N Highest common factor of a pair of successive terms of A076919.
%p A076920 := proc(nmax) local a,b,k; a := [1,2] ; b := [1] ; while nops(b) < nmax do k := op(-1,a)+1 ; while gcd(k,op(-1,a)) <= 1 or gcd(k,op(-1,a)) = gcd(op(-1,a),op(-2,a)) do k := k+1 ; od ; b := [op(b),gcd(k,op(-1,a))] ; a := [op(a),k] ; od ; RETURN(b) ; end: A076920(80) ; # _R. J. Mathar_, Jul 01 2007
%t f[1] = 1; f[2] = 2; (* f is A076919 *)
%t f[n_] := f[n] = Module[{k}, For[k = f[n-1] + 1, True, k++, If[GCD[f[n-1], f[n-2]] != GCD[k, f[n-1]] && GCD[k, f[n-1]] > 1, Return[k]]]];
%t GCD @@@ Partition[Table[f[n], {n, 1, 81}], 2, 1] (* _Jean-François Alcover_, Oct 25 2023 *)
%Y Cf. A076919.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Oct 17 2002
%E More terms from _R. J. Mathar_, Jul 01 2007
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