Re:Another theme of concatenated integers.

>>** I just spotted an error, it should be 277! **
>> at end of post
>>
>>And now not only a triangle number connection to
>>1234567891011..n, but a factorial connection as well!
>
>>1234567891011 == r (mod 11!)
>
>>1234567891011121314151617181920
>>212223242526272829 == r (mod 29!)
>
>>As the terms in these integers gets larger watch the trailing digits of (r)
>>See how they start to match up with the trailing digits of 12345..n
>>and increase in count as you add more terms to the integer.
>>
>>Below a much larger example --
>
>>12345678910111213141516171819202122232425262728293
>>03132333435363738394041424344454647484950515253545
>>55657585960616263646566676869707172737475767778798
>>08182838485868788899091929394959697989910010110210
>>31041051061071081091101111121131141151161171181191
>>20121122123124125126127128129130131132133134135136
>>13713813914014114214314414514614714814915015115215
>>31541551561571581591601611621631641651661671681691
>>70171172173174175176177178179180181182183184185186
>>18718818919019119219319419519619719819920020120223
>>20420520620720820921021121221321421521621721821922
>>02212222232242252262272282292302312322332342352362
>>37238239240241242243244245246247248249250251252253
>>25425525625725825926026126226326426526626726826927
>>0271272273274275276277 == r (mod 277!)
>
>>(r) here has a 68 trailing digit match.
>
>>I bet no one can explain this one!
>
>>Dan

>The factorials have more and more factors of 10, so >when you mod out
>by a high factorial, you are also modding out by a high >power of 10,
>so the digit match is automatic.

>In the prime factorization of 277!, there are 273 >factors of 2, and 68
>factors of 5. It follows that 277! has 68 factors of >10, and therefore
>68 trailing zeros.

>Hence, the fact that you got a 68 digit match is not at >all
>surprising.

>quasi

Nice explanation about a factorial divisor!
I would have lost that bet.:-(

Still no one has acknowledged the triangle number connection to these integers 1234567891011...?

Is it that I am not explaining it correctly or is
there an obvious explanation that I am missing?

Thanks for the explanation.

Dan

>277!=``(2)^273)(5)^68*``(7)^44*``(11)^27*``(13)^22*
>(17)^16*``(19)^14*``(23)^12*``(29)^9*``(31)^8*``(37)^7*(41)^6*``(43)^6*``(47)^5*``(53)^5*``(59)^4*``(61)^4*``(67)^4*``(71)^3*``(73)^3*``(79)^3*``(83)^3*``(89)^3*``(97)^2*``(101)^2*``(103)^2*``(107)^2*``(109)^2*``(113)^2*``(127)^2*``(131)^2*``(137)^2*``(139)*``(149)*``(151)>*``(157)*``(163)*``(167)*``(173)*``(179)*``(181)*``(191)>*``(193)*``(197)*``(199)*``(211)*``(223)*``(227)*``(229)>*``(233)*``(239)*``(241)*``(251)*``(257)*``(263)*``(269)>*``(271)*``(277)

>quasi
.

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