A247004 Denominator of (n+4)/gcd(n, 4)^2, a 16-periodic sequence that associates A061037 with A106617.

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

Author

Jean-François Alcover and Paul Curtz, Sep 09 2014

Keywords

• nonn
• easy

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.

Examples

			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];
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• 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).

Crossrefs

Cf. A060819, A061037, A106617, A109008, A188134, A213268.

Programs

Magma

[Denominator((n+4)/Gcd(n,4)^2): n in [0..100]]; // G. C. Greubel, Aug 05 2018

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}]

PARI

for(n=0,100, print1(denominator((n+4)/gcd(n,4)^2), ", ")) \\ G. C. Greubel, Aug 05 2018

Formula

A247004 = A060819 / A109008.

(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