login
A247004
Denominator of (n+4)/gcd(n, 4)^2, a 16-periodic sequence that associates A061037 with A106617.
1
4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2
OFFSET
0,1
COMMENTS
This sequence may also be defined as the denominators of A061037(n+3)/(n+1), or also as A060819 / A109008.
One can notice that the analog numerators [numerators of (n+4)/gcd(n, 4)^2] are A106617 left-shifted 4 places.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
FORMULA
(n+4) / gcd(n, 4)^2 = A188134(n+4) / 4. - Michael Somos, Sep 12 2014
a(n) = a(n+16) = a(-n), a(2*n + 1) = 1 for all n in Z. - Michael Somos, Sep 13 2014
EXAMPLE
Fractions begin:
1/4, 5, 3/2, 7, 1/2, 9, 5/2, 11, 3/4, 13, 7/2, 15, 1, 17, 9/2, 19,
5/4, 21, 11/2, 23, 3/2, 25, 13/2, 27, 7/4, 29, 15/2, 31, 2, 33, 17/2, 35,
...
Numerators begin:
1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19,
5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 2, 33, 17, 35,
...
Periodic part = [4, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1];
MATHEMATICA
a[n_] := (n+4)/GCD[n, 4]^2 // Denominator; Table[a[n], {n, 0, 100}]
(* or: *)
Table[{1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4}[[Mod[n, 16, 1]]], {n, 0, 100}]
PROG
(PARI) for(n=0, 100, print1(denominator((n+4)/gcd(n, 4)^2), ", ")) \\ G. C. Greubel, Aug 05 2018
(Magma) [Denominator((n+4)/Gcd(n, 4)^2): n in [0..100]]; // G. C. Greubel, Aug 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved