3909511 = 5^3 + 5^9 + 5^0 + 5^9 + 5^5 + 5^1 + 5^1 から始める「整数の累乗和」の話
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- いいね！0
Algebra Etc.
@AlgebraFact
3909511 = 5^3 + 5^9 + 5^0 + 5^9 + 5^5 + 5^1 + 5^1 via http://t.co/42WsRJLt
2012-02-20 23:43:27
Jim Wilder
@wilderlab
A smaller one- 4624: 4^4 + 4^6 + 4^2 + 4^4... do these numbers have a name? RT @JohnDCook: Monday morning math puzzle http://t.co/6VWWBhM0
2012-02-21 01:54:26
Republic of Mathematics
@republicofmath
Solutions n, b to n=dk...d0 (base 10) & b^dk+...+b^d0=n. 12=3^1+3^2, 4624=4^4+4^6+4^2+4^4, 595968=4^5+4^9+4^5+4^9+4^6+4^8 ...?
2012-02-21 03:19:49
Republic of Mathematics
@republicofmath
Call integer b >1 "sweet" if there's n=dk...d0 (base 10) with b^dk+...b^d0=n. 3 ,4, 5 are sweet: 12 (b=3), 4624 (b=4), 3909511 (b=5)
2012-02-21 03:27:39
Jim Wilder
@wilderlab
@republicofmath - 13177388 = 7^1 + 7^3 + 7^1 + 7^7 + 7^7 + 7^3 + 7^8 + 7^8
2012-02-21 04:23:57
Republic of Mathematics
@republicofmath
Wahoo! Sweet! @wilderlab 13177388 = 7^1 + 7^3 + 7^1 + 7^7 + 7^7 + 7^3 + 7^8 + 7^8
2012-02-21 06:40:09
Alexander Bogomolny
@CutTheKnotMath
Yes, indeed. @republicofmath WahooI Sweet @wilderlab 13177388 = 7^1 + 7^3 + 7^1 + 7^7 + 7^7 + 7^3 + 7^8 + 7^8
2012-02-21 06:45:48
Jim Wilder
@wilderlab
Awesome! And another: 52135640 = 19^5 + 19^2 + 19^1 + 19^3 + 19^5 + 19^6 + 19^4 + 19^0 MT @republicofmath: @wilderlab 1033=8^1+8^0+8^3+8^3
2012-02-21 09:38:48
Republic of Mathematics
@republicofmath
You magician, you! @wilderlab And another: 52135640 = 19^5 + 19^2 + 19^1 + 19^3 + 19^5 + 19^6 + 19^4 + 19^0
2012-02-21 09:48:15
Republic of Mathematics
@republicofmath
Here's an interesting twist: 14 = (-2)^1+(-2)^4 @wilderalb
2012-02-21 09:52:25
Jim Wilder
@wilderlab
Beautiful! RT @republicofmath: Here's an interesting twist: 14 = (-2)^1+(-2)^4 @wilderlab
2012-02-21 09:53:51
Republic of Mathematics
@republicofmath
And 12885 = (-3)^1+(-3)^2+(-3)^8+(-3)^8+(-3)^5 @wilderlab
2012-02-21 09:53:52
Jim Wilder
@wilderlab
Ha! You are owning me! That one is my favorite! RT @republicofmath: 111=37^1+37^1+37^1 LOL!! @wilderlab
2012-02-21 10:33:38
Republic of Mathematics
@republicofmath
Up to n=10^9 could find no n=d_k...d_0 such that 6^d_k+...+6^d_0 = n @wilderlab
2012-02-22 01:58:19
Jim Wilder
@wilderlab
I love that one too! RT @republicofmath: @wilderlab One that didn't come immediately to mind but should have: 10 = 9^1 + 9^0 Funny!
2012-02-22 06:21:36
Republic of Mathematics
@republicofmath
397612=3^2+9^1+7^6 +6^7+1^9+2^3 @wilderlab 48625=4^5+8^2+6^6+2^8+5^4 where exponents run reverse to the bases
2012-02-22 08:42:59
Jim Wilder
@wilderlab
Trying to close out research project, but beautiful! MT @republicofmath 397612=3^2+9^1+7^6 +6^7+1^9+2^3 @wilderlab 48625=4^5+8^2+6^6+2^8+5^4
2012-02-22 08:46:36
Jim Wilder
@wilderlab
Can you elaborate with soln on the first set? MT @republicofmath @wilderlab permute digits of n, raise digits of n to permuted- 1364 & 6143
2012-02-22 09:24:13
Jim Wilder
@wilderlab
@republicofmath - ok... get ready for a laugh- 4096 = 4^6 + 0^9
2012-02-22 12:17:01
Republic of Mathematics
@republicofmath
936627 has a permutation 296637 & 9^2 + 3^9 + 6^6 + 6^ + 2^3 + 7^7 = 936627 @wilderlab @BenVitale
2012-02-23 20:39:52
Benjamin Vitale
@BenVitale
Powers are the same as the digits & the reverse http://t.co/Ja8JMQzO via @wordpressdotcom #mathchat #math
2012-02-26 04:15:38
Jim Wilder
@wilderlab
To expand on an ascending number sequence, look at the exponents: 135 = 1^1 + 3^2 + 5^3 and 175 = 1^1 + 7^2 + 5^3 @BenVitale #mathchat
2012-02-26 04:32:02