login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213923 Minimal lengths of formulas representing n only using addition, multiplication and the constant 1. 5
1, 3, 5, 7, 9, 9, 11, 11, 11, 13, 15, 13, 15, 15, 15, 15, 17, 15, 17, 17, 17, 19, 21, 17, 19, 19, 17, 19, 21, 19, 21, 19, 21, 21, 21, 19, 21, 21, 21, 21, 23, 21, 23, 23, 21, 23, 25, 21, 23, 23, 23, 23, 25, 21, 23, 23, 23, 25, 27, 23, 25, 25, 23, 23, 25, 25, 27, 25, 27, 25, 27, 23, 25, 25, 25, 25, 27, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Shalosh B. Ekhad, Everything About Formulas Representing Integers Using Additions and Multiplication for integers from 1 to 8000.

Edinah K. Ghang, Doron Zeilberger, Zeroless Arithmetic: Representing Integers ONLY using ONE, arXiv:1303.0885 [math.CO], 2013

FORMULA

a(n) = 2*A005245(n)+1.

EXAMPLE

a(3) = 5 because for n = 3, the minimum is length = 5, formula = "11+1+" or "111++".

MAPLE

with(numtheory):

a:= proc(n) option remember;

       1+ `if`(n=1, 0, min(seq(a(i)+a(n-i), i=1..n/2),

       seq(a(d)+a(n/d), d=divisors(n) minus {1, n})))

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Mar 07 2013

MATHEMATICA

a[n_] := a[n] = 1 + If[n == 1, 0, Min[Join[Table[a[i] + a[n-i], {i, 1, n/2}], Table[a[d] + a[n/d], {d, Divisors[n] ~Complement~ {1, n}}]]]]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Feb 01 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A005245, A214833.

Sequence in context: A265509 A265527 A217250 * A218452 A007731 A306590

Adjacent sequences:  A213920 A213921 A213922 * A213924 A213925 A213926

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Mar 06 2013

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 September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)