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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 *)
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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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_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Oct 17 2002
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 (mathar(AT)strw.leidenuniv.nl), _, Jul 01 2007
More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Jul 01 2007
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) ; - Richard R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 01 2007
nonn,new
nonn
More terms from Richard R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 01 2007
The highest Highest common factor of a pair of successive members 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
Observations (1): a(5n+3) = 4, (2): a(5n + 2) = 2 = a(5n + 4) (3): the second onwards string "2,4,2" is always sandwitched between two primes.(proof!!)
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) ; - Richard J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 01 2007
more,nonn,new
nonn
More terms from Richard J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 01 2007
The highest common factor of pair of successive members 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
1,2
Observations (1): a(5n+3) = 4, (2): a(5n + 2) = 2 = a(5n + 4) (3): the second onwards string "2,4,2" is always sandwitched between two primes.(proof!!)
Cf. A076919.
more,nonn
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 17 2002
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