login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261790 Regular triangle read by rows: T(n,k) is the least positive number m such that k*m and k*m*(m+1)/2 are both divisible by n, with 0<=k<=n and T(0,0)=1. 0
1, 1, 1, 1, 4, 1, 1, 3, 3, 1, 1, 8, 4, 8, 1, 1, 5, 5, 5, 5, 1, 1, 12, 3, 4, 3, 12, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 16, 8, 16, 4, 16, 8, 16, 1, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 1, 20, 5, 20, 5, 4, 5, 20, 5, 20, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 1, 24, 12, 8, 3, 24, 4, 24, 3, 8, 12, 24, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(360,k) is the number of steps for a Logo turtle to return to the same orientation and same heading when using the INSPIR program with starting angle and angular increment k.

REFERENCES

Harold Abelson and Andrea diSessa, Turtle Geometry, Artificial Intelligence Series, MIT Press, July 1986, pp. 20 and 36.

Brian Hayes, La tortue vagabonde, in Récréations Informatiques, Pour La Science, Belin, Paris, 1987, pp. 24-28, in French, translation from Computer Recreations, February 1984, Scientific American Volume 250, Issue 2.

LINKS

Table of n, a(n) for n=0..90.

EXAMPLE

Triangle starts:

1;

1, 1;

1, 4, 1;

1, 3, 3, 1;

1, 8, 4, 8, 1;

1, 5, 5, 5, 5, 1;

1, 12, 3, 4, 3, 12, 1;

1, 7, 7, 7, 7, 7, 7, 1;

1, 16, 8, 16, 4, 16, 8, 16, 1;

...

MATHEMATICA

{1}~Join~Table[m = 1; While[Nand[Mod[k m, n] == 0, Mod[k m (m + 1)/2, n] == 0], m++]; m, {n, 12}, {k, 0, n}] // Flatten (* Michael De Vlieger, Sep 01 2015 *)

PROG

(PARI) T(n, k) = {if (n==0, return (1)); m=1; while(((k*m*(m+1)/2) % n) || (k*m % n), m++); m; }

row(n) = vector(n+1, k, k--; T(n, k));

tabl(nn) = for(n=0, nn, print(row(n)));

CROSSREFS

Cf. A011772, A022998 (2nd column).

Sequence in context: A087963 A274540 A010323 * A174834 A100642 A255511

Adjacent sequences:  A261787 A261788 A261789 * A261791 A261792 A261793

KEYWORD

nonn,tabl

AUTHOR

Michel Marcus, Sep 01 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 23 18:42 EDT 2017. Contains 286926 sequences.