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

[Jonathan Post]

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
>