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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074171 a(1) = 1. For n >= 2, a(n) is either a(n-1)+n or a(n-1)-n; we only use the minus sign if a(n-1) is prime. E.g. since a(2)=3 is prime, a(3)=a(2)-3=0. 2
1, 3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, 1269, 1320, 1372, 1425, 1479 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In spite of the definition, this is simply 1, 3, then numbers of the form n*(n+7)/2 (A055999). In other words, a(n) = (n-3)(n+4)/2 for n >= 3. The proof is by induction: For n>3, a(n-1) = (n-4)(n+3)/2 is composite, so a(n) = a(n-1) + n = (n-3)(n+4)/2. - Dean Hickerson, T. D. Noe, Paul C. Leopardi, Labos E. and others, Oct 04 2004

If a 2-set Y and a 3-set Z, having one element in common, are subsets of an n-set X then a(n) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 03 2007

LINKS

Table of n, a(n) for n=1..54.

Milan Janjic, Two Enumerative Functions

FORMULA

a[1] = 1, a[2] = 3; a[n+1] = a[n]+n if a[n] is not a prime; a[n+1] = a[n]-n if a[n] is prime.

EXAMPLE

a(1) = 1

a(2) = a(1) + 2 = 3, which is prime, so

a(3) = a(2) - 3 = 0, which is not prime, so

a(4) = a(3) + 4 = 4, which is not prime, etc.

MATHEMATICA

{ta={1, 3}, tb={{0}}}; Do[s=Last[ta]; If[PrimeQ[s], ta=Append[ta, s-n]]; If[ !PrimeQ[s], ta=Append[ta, s+n]]; Print[{a=Last[ta], b=(n-3)*(n+4)/2, a-b}]; tb=Append[tb, a-b], {n, 3, 100000}]; {ta, {tb, Union[tb]}} (Labos)

CROSSREFS

Cf. A074170, A055999.

Sequence in context: A068630 A079406 A068627 * A180657 A094665 A052439

Adjacent sequences:  A074168 A074169 A074170 * A074172 A074173 A074174

KEYWORD

easy,nonn

AUTHOR

Amarnath Murthy, Aug 30 2002

EXTENSIONS

More terms from Jason Earls, Sep 01 2002

More terms from Labos Elemer, Oct 07 2004

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 October 19 22:00 EDT 2018. Contains 316378 sequences. (Running on oeis4.)