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A239663 a(n) is the smallest number k such that the symmetric representation of sigma(k) has n parts. 16
1, 3, 9, 21, 63, 147, 357, 903, 2499, 6069, 13915, 29095, 59455, 142945, 320045, 643885, 1367465, 3287735 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For more information about the symmetric representation of sigma see A237270, A237593.

This sequence of (first occurrence of) parts appears to be strictly increasing in contrast to sequence A250070 of (first occurrence of) maximum widths. - Hartmut F. W. Hoft, Dec 09 2014

Where records occur in A237271. - Omar E. Pol, Dec 27 2016

It appears that all terms are odd numbers. - Omar E. Pol, Oct 14 2018

LINKS

Table of n, a(n) for n=1..18.

Hartmut F. W. Hoft, Procedural implementation for extension values

EXAMPLE

------------------------------------------------------

n       a(n)     A239665                  A266094(n)

------------------------------------------------------

1        1       [1]                           1

2        3       [2, 2]                        4

3        9       [5, 3, 5]                    13

4       21       [11, 5, 5, 11]               32

5       63       [32, 12, 16, 12, 32]        104

...

For n = 3 the symmetric representation of sigma(9) = 13 contains three parts [5, 3, 5] as shown below:

.

.     _ _ _ _ _ 5

.    |_ _ _ _ _|

.              |_ _ 3

.              |_  |

.                |_|_ _ 5

.                    | |

.                    | |

.                    | |

.                    | |

.                    |_|

.

MATHEMATICA

(* a239663[] permits computation in intervals *)

(* Function a237270[] is defined in A237270 *)

(* variable "list" contains the first occurences up to m *)

a239663[list_, {m_, n_}]:=Module[{firsts=list, g=Length[list], i, p}, For[i=m, i<=n, i++, p=Length[a237270[i]]; If[p>g, AppendTo[firsts, i]; g=p]]; firsts]

a239663[{1}, {1, 1000}] (* computes the first 8 values *)

(* Hartmut F. W. Hoft, Jul 08 2014 *)

CROSSREFS

Row 1 of A240062.

Cf. A000203, A196020, A236104, A235791, A237048, A237270, A237271, A237591, A237593, A238443, A239657, A239660, A239665, A239931-A239934, A245092, A262626, A266094.

Sequence in context: A146416 A260185 A307105 * A004667 A237122 A326313

Adjacent sequences:  A239660 A239661 A239662 * A239664 A239665 A239666

KEYWORD

nonn,more,hard

AUTHOR

Omar E. Pol, Mar 23 2014

EXTENSIONS

a(6)-a(8) from Michel Marcus, Mar 28 2014

a(9) from Michel Marcus, Mar 29 2014

a(10)-a(11) from Michel Marcus, Apr 02 2014

a(12) from Hartmut F. W. Hoft, Jul 08 2014

a(13)-a(18) from Hartmut F. W. Hoft, Dec 09 2014

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)