login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A255051 a(1)=1, a(n+1) = a(n)/gcd(a(n),n) if this GCD is > 1, else a(n+1) = a(n) + n + 1. 4
1, 3, 6, 2, 1, 7, 14, 2, 1, 11, 22, 2, 1, 15, 30, 2, 1, 19, 38, 2, 1, 23, 46, 2, 1, 27, 54, 2, 1, 31, 62, 2, 1, 35, 70, 2, 1, 39, 78, 2, 1, 43, 86, 2, 1, 47, 94, 2, 1, 51, 102, 2, 1, 55, 110, 2, 1, 59, 118, 2, 1, 63, 126, 2, 1, 67, 134, 2, 1, 71, 142, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A somehow "trivial" variant of A133058 and A255140, both of which have very similar definitions, but enter 4-periodic loops only at later indices.

There could be two motivated values for an initial term: either a(0)=0 which would yield a(1)=1 and the following values via the recursion formula, or a(0)=2 according to the general formula for a(4k).

LINKS

Table of n, a(n) for n=1..73.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

FORMULA

a(4k+1) = 1, a(4k+2) = 4k+3, a(4k+3) = 2*a(4k+2) = 8k+6, a(4k) = 2.

G.f.: x*(1 + 3*x + 6*x^2 + 2*x^3 - x^4 + x^5 + 2*x^6 - 2*x^7)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2). - Bruno Berselli, Feb 16 2015

a(n) = ( 2*(3 + (-1)^n) - (2 - 3*n + n*(-1)^n)*(1 - (-1)^((n-1)*n/2)) )/4. - Bruno Berselli, Feb 16 2015

EXAMPLE

a(2) = a(1)+2 = 3, a(3) = a(2)+3 = 6, a(4) = a(3)/3 = 2, a(5) = a(4)/2 = 1;

a(6) = a(5)+6 = 7, a(7) = a(6)+7 = 14, a(8) = a(7)/7 = 2, a(9) = a(8)/2 = 1; ...

MATHEMATICA

Table[(2 (3 + (-1)^n) - (2 - 3 n + n (-1)^n) (1 - (-1)^((n - 1) n/2)))/4, {n, 1, 80}] (* Bruno Berselli, Feb 16 2015 *)

nxt[{n_, a_}]:={n+1, If[GCD[a, n]>1, a/GCD[a, n], a+n+1]}; Transpose[ NestList[ nxt, {1, 1}, 80]][[2]] (* or *) LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {1, 3, 6, 2, 1, 7, 14, 2}, 80] (* Harvey P. Dale, Oct 13 2015 *)

PROG

(PARI) (A255051_upto(N)=vector(N, n, if(gcd(N, n-1)>1, N\=gcd(N, n-1), N+=n)))(99) \\ simplified by M. F. Hasler, Jan 11 2020

(PARI) A255051(n)=if(n%4>1, if(bittest(n, 0), n*2, n+1), 2-bittest(n, 0)) \\ M. F. Hasler, Feb 18 2015

(Magma) &cat [[1, 4*n+3, 8*n+6, 2]: n in [0..20]]; // Bruno Berselli, Feb 16 2015

CROSSREFS

Cf. A133058, A255140.

Sequence in context: A016551 A238555 A176034 * A145896 A159963 A120907

Adjacent sequences: A255048 A255049 A255050 * A255052 A255053 A255054

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Feb 15 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 07:08 EST 2022. Contains 358673 sequences. (Running on oeis4.)