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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182987 Least a+b such that ab=A002110(n), the product of the first n primes; a,b being positive integers. 5
2, 3, 5, 11, 29, 97, 347, 1429, 6229, 29873, 160879, 895681, 5448239, 34885673, 228759799, 1568299433, 11417382973, 87698582693, 684947829299, 5606539600699, 47241542381273, 403631914511993, 3587558929043927, 32684217334524347, 308342289648328511, 3036819365023723883 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Original definition (not applicable for n=0 and n=1, but equivalent for n>=2):

Let p(S) be product of integers in S. a(n) is minimum of p(S_1) + p(S_2) over all partitions of first n primes into sets S_1 and S_2.

Also: Least integer such that a(n)^2-4*A002110(n) is a square. [David Broadhurst, Sep 20 2011]

The integers a,b are the two median divisors of primorial(n), a=A060795(n)=A060775(A002110(n)) and b=A060796(n)=A033677(A002110(n)). (For n=0, a=b=1 of course.) - M. F. Hasler, Sep 20 2011

LINKS

Table of n, a(n) for n=0..25.

D. Broadhurst, Re: adding to prime number [primes in A182987], primenumbers group, Sep 20 2011.

FORMULA

a(n) = A060795(n) + A060796(n). - M. F. Hasler, Sep 20 2011

EXAMPLE

a(3) = 11 = min{ 2*3 + 5 = 11, 2*5 + 3 = 13, 3*5 + 2 = 17 }

Or, a(3) = 11 = min { 1+30, 2+15, 3+10, 5+6 } because A002110(3) = 2*3*5 = 30 = 2*15 = 3*10 = 5*6.

MATHEMATICA

a[0] = 2; a[n_] := Module[{m = Times @@ Prime[Range[n]]}, For[an = 2 Floor[Sqrt[m]] + 1, an <= m + 2, an += 2, If[IntegerQ[Sqrt[an^2 - 4 m]], Return[an]]]]; Table[an = a[n]; Print[an]; an, {n, 0, 25}] (* Jean-Fran├žois Alcover, Oct 20 2016, adapted from PARI *)

PROG

(PARI) A182987(n)={n=divisors(prod(i=1, n, prime(i))); n[max(#n\2, 1)]+n[#n\2+1]}  \\ M. F. Hasler, Sep 20 2011

(PARI) A182987(n)={ n||return(2); my(m=prod(k=1, n, prime(k))); forstep(a=2*sqrtint(m)+1, m+2, 2, issquare(a^2-4*m) & return(a)) }  \\ M. F. Hasler, following an idea from David Broadhurst, Sep 20 2011

CROSSREFS

Cf. A173631.

Sequence in context: A265418 A190197 A173631 * A087580 A072535 A073680

Adjacent sequences:  A182984 A182985 A182986 * A182988 A182989 A182990

KEYWORD

nonn

AUTHOR

Risto Kauppila, Feb 06 2011

EXTENSIONS

First term and example corrected, as empty sets have product 1, by Phil Carmody, Sep 20 2011

Simpler definition and extension to n=0 by M. F. Hasler, Sep 20 2011

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)