# [seqfan] Re: Essicran Numbers

Bob Selcoe rselcoe at entouchonline.net
Tue Oct 27 03:50:53 CET 2015

```Hi Eric & Seqfans,

Generally, let the digit sum of X=D; then if the least residue of 2X_mod_D
is a member of S where S is 0 and the partial sums of the digits of X
(excluding the 1s digit), then the number is Essicran.

So X=13: S={0,1}, D=4; 26mod4 == 2 not in S, therefore 13 != Essicran.

X=12: S={0,1}, D=3; 24mod3 == 0 therefore 12 = Essicran.

X=2015: S={0,2,3}, D=8; 4030mod8 == 6 not in S, therefore 2015 != Essicran.

X=11237; S={0,1,2,4,7}, D=14;   22474mod14 == 4, therefore 11237 = Essicran.

Cheers,
Bob Selcoe

--------------------------------------------------
From: "Eric Angelini" <Eric.Angelini at kntv.be>
Sent: Monday, October 26, 2015 6:54 PM
To: "Sequence Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Essicran Numbers

> Hello SeqFans,
>
> An Essicran integer X turns into -X
> after a few subtractions.
>
> If you iterate 2015-2-0-1-5-2-0-1-5-2-0-1-5-2-0-1-5-2... long enough
> and reach at some stage -2015, then
> you have a "hit"... and an Essicran number.
>
> 1 is (of course) a EN
> 2 is a EN
> 3 is a EN, as are 4,5,5,7,8,9,10,11;
> 12 is a EN
> 13 is not because the successive
> subtractions -1 and -3 never hit
> -13 at some point hereunder:
>
> 13-1=12-3=9-1=8-3=5-1=4-3=1-1=0
> 0-3=-3-1=-4-3=-7-1=-8-3=-11-1=-12-3=-15... miss!
>
> "Narcissic" (or Armstrong) numbers
> already exist in the OEIS -- this is
> why I've coined "Essicran".
>
> Best,
> É.
>
>
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>
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>
```