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A226272
Distinct numbers that can be written as u^v, where u and v are not necessarily distinct digits of n in decimal representation, table read by rows.
3
1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 0, 1, 1, 1, 2, 4, 1, 3, 27, 1, 4, 256, 1, 5, 3125, 1, 6, 46656, 1, 7, 823543, 1, 8, 16777216, 1, 9, 387420489, 0, 1, 4, 1, 2, 4, 4, 4, 8, 9, 27, 4, 16, 256, 4, 25, 32, 3125, 4, 36, 64, 46656
OFFSET
0,3
COMMENTS
Row lengths: A226273;
T(n,k) <= 9^9 = 387420489;
largest term of n-th row = A054055(n)^A054055(n);
row(n) is contained in row(10*n+d), 0 <= d <= 9;
see A226277 for numbers m such that m is contained in m-th row.
LINKS
EXAMPLE
. n row(n) A226273(n)
. --- --------------------- ----------------------- ----------
. 0 [1] {0^0} 1
. 1 [1] {1^1} 1
. 2 [4] {2^2} 1
. 3 [27] {3^3} 1
. 4 [256] {4^4} 1
. 5 [3125] {5^5} 1
. 6 [46656] {6^6} 1
. 7 [823543] {7^7} 1
. 8 [16777216] {8^8} 1
. 9 [387420489] {9^9} 1
. 10 [0,1] {0^1, 0^0=1^0=1^1} 2
. 11 [1] = row(1) {1^1} 1
. 12 [1,2,4] {1^1=1^2, 2^1, 2^2} 3
. 13 [1,3,27] {1^1=1^3, 3^1, 3^3} 3
. 14 [1,4,256] {1^1=1^4, 4^1, 4^4} 3
. 15 [1,5,3125] {1^1=1^5, 5^1, 5^5} 3
. 16 [1,6,46656] {1^1=1^6, 6^1, 6^6} 3
. 17 [1,7,823543] {1^1=1^7, 7^1, 7^7} 3
. 18 [1,8,16777216] {1^1=1^8, 8^1, 8^8} 3
. 19 [1,9,387420489] {1^1=1^9, 9^1, 9^9} 3
. 20 [0,1,4] {0^2, 0^0=2^0, 2^2} 3
. 21 [1,2,4] = row(12) {1^1=1^2, 2^1, 2^2} 3
. 22 [4] = row(2) {2^2} 1
. 23 [4,8,9,27] {2^2, 2^3, 3^2, 3^3} 4
. 24 [4,16,256] {2^2, 2^4=4^2, 4^4} 3
. 25 [4,25,32,3125] {2^2, 5^2, 2^5, 5^5} 4
. 26 [4,36,64,46656] {2^2, 6^6, 2^6, 6^6} 4
. 27 [4,49,128,823543] {2^2, 7^2, 2^7, 7^7} 4
. 28 [4,64,256,16777216] {2^2, 8^2, 2^8, 8^8} 4
. 29 [4,81,512,387420489] {2^2, 9^2, 2^9, 9^9} 4
. 30 [0,1,27] {0^3, 0^0=3^0, 3^3} 3 .
PROG
(Haskell)
import Data.List (nub, sort)
a226272 n k = a226272_tabf !! n !! k
a226272_row n = sort $ nub [u ^ v | u <- digs, v <- digs]
where digs = nub $ map (read . return) $ show n
a226272_tabf = map a226272_row [0..]
CROSSREFS
Cf. A000312.
Sequence in context: A324808 A245413 A344658 * A086756 A061510 A045512
KEYWORD
nonn,base,tabf
AUTHOR
Reinhard Zumkeller, Jul 09 2013
STATUS
approved