[seqfan] Re: Numbers n such that the decimal representation of n is contained as substring in that of the n-th pentagonal number.

Claudio Meller claudiomeller at gmail.com
Tue Jul 27 03:22:34 CEST 2010


Hi John
the first terms are:

0, 1, 5, 7, 25, 67, 482, 551, 625, 667, 2937, 6667, 9284, 9376, 9649, 48179,
49900, 55712, 66667, 89517, 90625, 161579, 631206, 666667, 890625

Claudio


2010/7/26 Jonathan Post <jvospost3 at gmail.com>

> I've found one more.  But, doing this "by hand" gives me little
> confidence that I've not missed any smaller ones.
>
> %I A000001
> %S A000001 0,1,5,7,25,67,482,667
> %N A000001 Numbers n such that the decimal representation of n is
> contained as substring in that of the n-th pentagonal number.
> %C A000001 This is to pentagonal numbers A000326 as A119238 is to
> triangular numbers A000217 and as A018834 is to squares A000290.
> %e A000001 The 5th pentagonal number, 35, which contains 5.
> %e A000001 The 7th pentagonal number, 70, which contains 7.
> %e A000001 The 25th pentagonal number, 925, which contains 25.
> %e A000001 The 67th pentagonal number, 6700, which contains 67.
> %e A000001 The 482nd pentagonal number, 348245, which contains 482.
> %e A000001 The 667th pentagonal number, 667000, which contains 667000.
> %Y A000001 Cf. A000217, A000290, A000326, A018834, A119238.
> %K A000001 base,more,nonn
> %O A000001 1,3
> %A A000001 Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 26 2010
>
>
> On Mon, Jul 26, 2010 at 5:45 PM, Jonathan Post <jvospost3 at gmail.com>
> wrote:
> > Before I submit this, as I've made errors in some recent submissions,
> > would anyone like to code it, and verify, correct, or extend it?
> >
> > %I A000001
> > %S A000001 0,1,5,7,25,67,482
> > %N A000001 Numbers n such that the decimal representation of n is
> > contained as substring in that of the n-th pentagonal number.
> > %C A000001 This is to pentagonal numbers A000326 as A119238 is to
> > triangular numbers A000217 and as A018834 is to squares A000290.
> > %e A000001 The 5th pentagonal number, 35, which contains 5.
> > %e A000001 The 7th pentagonal number, 70, which contains 7.
> > %e A000001 The 25th pentagonal number, 925, which contains 25.
> > %e A000001 The 67th pentagonal number, 6700, which contains 67.
> > %e A000001 The 482nd pentagonal number, 348245, which contains 482.
> > %Y A000001 Cf. A000217, A000290, A000326, A018834, A119238.
> > %K A000001 base,more,nonn
> > %O A000001 1,3
> > %A A000001 Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 26 2010
> >
> > I presume it interesting, as "base" sequences go, because it is the
> > analog of at least two exisiting sequences, and thus part of a larger
> > pattern.
> >
> > I'd prefer to be sure of this for 5-gonal numbers, as well as for
> > existing analog in 3-gonal and 4-gonal numbers, before going to more
> > elaborate sequences for k-gonal number with k>5.
> >
> > Best,
> >
> > Jonathan Vos Post
> >
>
>
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>
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>



-- 
Claudio
http://grageasdefarmacia.blogspot.com
http://todoanagramas.blogspot.com/
http://simplementenumeros.blogspot.com/



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