Math Is Fun Forum

Mathworld:

Then there are the Smith relatives, which are consecutive numbers that are also Smith numbers :
Smith brothers: eg, 728, 729
Smith triples: eg, 73615,73616,73617
Smith quads: eg, 4463535, 4463536, 4463537, 4463538
...etc.

Of course, the term 'Smith brothers' is not strictly correct, because, according to this article by that prolific writer, Anon Y. Mous, "all odd numbers are 'masculine' and all even numbers 'feminine' ", meaning that consecutive number gender alternates.

So you're related to the Smith family too?! Though distantly, as it seems to be in name only.

3757

3757 occurs at position 511 of concatenated consecutive Smith triangular numbers, whose string commences with the first such number.

AND, even furthermore still(!)......3757-511=3246 (ie, 2*3*541), which is also a Smith number:
3+2+4+6 = 2+3+5+4+1 = 15

Hi Bobby,

Your 3497 position at 12878 was correct, so you must have put in that same number again into your program instead of 3549. Anyway, 12878 + (3549-3497)*4 = 13086, not 13085.

I'll skip this round...to keep pace with the post# x 13 'rule'.

666 is also a 'Smith' number, and if the letters of that name are ascribed a value corresponding to their position in the alphabet (ie, a=1, b=2......z=26), the sum of those values is 69, which is a right or left 180° rotatable number.

3562

This is post #274

2 + 7 + 4 = 13....and 3562/13 = 274.

Btw, Bobby,  3549 occurs at position 13086 in Champernowne's number.

3510

ie, the 3rd of May this year.

Deduct today (28 April) = 5 days...and 3*5-10 = 5.

I counted 3419 to be the first four digits after the 6628th....but near the end I ran out of hairs on my arms that I was using to help me with the counting, so I might be wrong.

3432: 3*4+3-2 = 13

Hi Bobby,

I only got my 3354 in before you because, unlike you who slogged away at your construction, I just cut and pasted the info. I feel like a real heel!

3367: 3 - 3 + 6 + 7 = 13

3380: The 3380.net domain is available for purchase. This is a great chance for anyone wanting a domain name bearing a number that features so prominently on MIF!

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Hi Bobby,

Aah, I see.

I never learnt about dividing polynomials. Anyway, I worked my way to your answer with MIF's help.

Looks like I didn't interpret "remainder" correctly as applied to polynomial division...although I think it stands up mathematically when applying x = 30 to my polynomial and the divisors.

MIF says: "just put the remainder divided by the bottom polynomial as part of the answer", and so my answer becomes x + 36 + 346/(x-9).

For x = 30, 346/(x-9) is 16 remainder 10, and so still agrees with my misinterpreted understanding of "remainder".

That puts a whole new light onto your problem. Not sure if I can manage to solve it now.

Hi Bobby,

Something to do with Octal (the number after 8 is 11) or binary (255 = 11111111), maybe?

I tried my longhand idea...and I was wrong. Too much mental arithmetic involved, and too easy to make a mistake. Also too easy to miss some. It can be done...with some sweat and tears (unless you're wide awake for this sort of thing).

I had another idea in mind, but that is a bit tricky too and involves quite a few additions. I think my original idea with LB, which was quite easy to set up and solves quickly, is my best option so far.

Btw, is my answer correct?

Hi Bobby,