A076920 Highest common factor of a pair of successive terms of A076919.
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, 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, 17, 83, 2, 4, 2, 751, 3, 2, 1129, 3, 2, 4, 2, 1699, 3, 2, 2551, 3, 2, 7
Offset: 1
Keywords
Crossrefs
Cf. A076919.
Programs
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Maple
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
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Mathematica
f[1] = 1; f[2] = 2; (* f is A076919 *) 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]]]]; GCD @@@ Partition[Table[f[n], {n, 1, 81}], 2, 1] (* Jean-François Alcover, Oct 25 2023 *)
Extensions
More terms from R. J. Mathar, Jul 01 2007