[seqfan] Re: Divisibility by primes

[Benoît Jubin]

The corresponding sequence in base 2 is empty, and in base 3, it is given by
a_3(n) = (9^n-1)/2,
that is, numbers whose representation in base 3 is 111......111 with an
even number of 1's.
This is particular since the base itself is prime.
It might be worth computing the sequence in bases 4 and 5.

Benoit


On Fri, Apr 10, 2015 at 7:56 PM, Reinhard Zumkeller <
reinhard.zumkeller at gmail.com> wrote:

> https://oeis.org/draft/A256786
>
> Best regards
> Reinhard
>
> 2015-04-10 16:53 GMT+02:00 Lars Blomberg <lars.blomberg at visit.se>:
>
> > Hello,
> >
> > I find the first few terms to be
> > 12, 14, 42, 55, 154, 222, 228, 714, 1122, 1196, 1212, 1414, 2112, 2142,
> > 2262, 3355, 4144, 4242, 5335, 5544, 5555, 6162, 9499, 11112, 11144,
> 11214,
> > 11424, 11466, 11622, 11818, 11914, 12222, 12882, 14112, 15554, 16666,
> > 21216, 21222, 21252, 21888, 22122, 22212, 22287, 24255, 24444, 25212,
> > 41174, 41244, 41412, 44114, 44142, 44226, 44744, 47124, 48944, 53625,
> > 55385, 57222, 62166, 62244, 63635, 66222, 66612, 67626, 68666, 69966,
> > 72114, 72267, 72777, 75735, 77112, 81282, 84854, 85272, 88122, 88844,
> > 99222, 99912, 99935, 111188, 111222, 112122, 112212, 112224, 114114,
> > 116116, 118218, 119922, 121122, 121182, 121212, 121422, 121992, 122112,
> > 122226, 122616, 124488, 126126, 129444, 141414, 142212, 142422, 142842,
> > 144144, 146146, 148428, 154154, 156156, 161226, 161616, 161772, 162162,
> > 164164, 166166, 182172, 182286, 188518, 211122, 211128, 211212, 211692,
> > 211812, 212112, 212142, 212772, 214242, 216216, 221112, 221214, 221424,
> > 221844, 222222, 222255, 222552, 222585, 222612, 224112, 225225, 225522,
> > 225555, 226122, 226512, 228228, 228855, 241122, 242214, 242424, 242949,
> > 244188, 246246, 252252, 255222, 255255, 255552, 261222, 261612, 262626,
> > 264264, 265122,
> >
> > And
> > a[1000] = 11299992
> > a[10000] = 555114252
> >
> > /Lars
> >
> > -----Ursprungligt meddelande-----
> > Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
> > Skickat: den 10 april 2015 13:02
> > Till: Sequence Discussion list
> > Ämne: [seqfan] Divisibility by primes
> >
> >
> > Hello SeqFans,
> > 12 is divisible by the 1st and the 2nd prime
> > 14 is divisible by the 1st and the 4th prime
> > 42 is divisible by the 4th and the 2nd prime ...
> > Are there many others?
> > (yes, an infinity: 222, 222222, 222222222, etc) Best, É.
> > Catapulté de mon aPhone
> >
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