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

0,1

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

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).

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

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

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

Sequence in context: A144870 A370211 A256252 * A010640 A244424 A322574

Adjacent sequences: A247001 A247002 A247003 * A247005 A247006 A247007

Keyword

nonn,easy

Author

Jean-François Alcover and Paul Curtz, Sep 09 2014

Status

approved