A226272 -id:A226272 - cp's OEIS frontend

A226273 Number of distinct values u^v, where u and v are digits occurring in decimal representation of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 4, 3, 4, 4, 4, 4, 4, 3, 3, 4, 1, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 1, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 1, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 1, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 1, 4, 4, 3, 3, 4, 4, 4, 4

Offset: 0

Reinhard Zumkeller, Jul 09 2013

Row lengths in table A226272;
a(n) <= 61; A171102(1) = 1023456789 is the smallest number m such that a(m) = 61.
a(n) = 61 for almost all n, in the sense that the natural density of n such that a(n) < 61 is 0. - Charles R Greathouse IV, May 13 2015

			See A226272.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

a226273 = length . a226272_row :: Integer -> Int

a(n)=if(n<9, return(1)); my(d=Set(digits(n)),v=List()); for(i=1,#d, for(j=1,#d, listput(v,d[i]^d[j]))); #Set(v) \\ Charles R Greathouse IV, May 13 2015

A226277 Numbers m of the form u^v where u and v are digits in decimal representation of m.

Original entry on oeis.org

1, 25, 3125, 4096, 15625, 19683, 46656, 59049, 78125, 117649, 279936, 1953125, 4782969, 5764801, 10077696, 387420489

Offset: 1

Reinhard Zumkeller, Jul 09 2013

a(n) occurs in a(n)-th row of table A226272.

			a(1) = 1 = 1^1;
a(2) = 25 = 5^2;
a(3) = 3125 = 5^5;
a(4) = 4096 = 4^6;
a(5) = 15625 = 5^6;
a(6) = 19683 = 3^9;
a(7) = 46656 = 6^6;
a(8) = 59049 = 9^5;
a(9) = 78125 = 5^7;
a(10) = 117649 = 7^6;
a(11) = 279936 = 6^7;
a(12) = 1953125 = 5^9;
a(13) = 4782969 = 9^7;
a(14) = 5764801 = 7^8;
a(15) = 10077696 = 6^9;
a(16) = 387420489 = 9^9.
256 = 2^8 = 4^4 is not a term, as neither 8 nor 4 occur in 256.

import Data.List (sort)
a226277 n = a226277_list !! (n-1)
a226277_list = sort [w | u <- [0..9], v <- [0..9], let w = u ^ v,
   "0123456789" !! u `elem` show w, "0123456789" !! v `elem` show w]

cp's OEIS Frontend

A226273 Number of distinct values u^v, where u and v are digits occurring in decimal representation of n.

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