

A074171


a(1) = 1. For n >= 2, a(n) is either a(n1)+n or a(n1)n; we only use the minus sign if a(n1) 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
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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) = (n3)(n+4)/2 for n >= 3. The proof is by induction: For n>3, a(n1) = (n4)(n+3)/2 is composite, so a(n) = a(n1) + n = (n3)(n+4)/2.  Dean Hickerson, T. D. Noe, Paul C. Leopardi, Labos E. and others, Oct 04 2004
If a 2set Y and a 3set Z, having one element in common, are subsets of an nset X then a(n) is the number of 3subsets 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, sn]]; If[ !PrimeQ[s], ta=Append[ta, s+n]]; Print[{a=Last[ta], b=(n3)*(n+4)/2, ab}]; tb=Append[tb, ab], {n, 3, 100000}]; {ta, {tb, Union[tb]}} (Labos)


CROSSREFS

Cf. A074170, A055999.
Sequence in context: A309764 A079406 A068627 * A180657 A094665 A309053
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



