A389849 Smallest number of the form a^b, with 1 < a and 1 < b and a != b, for which the digit sets of a^b and b^a share exactly n digits.

8, 25, 16, 1296, 2704, 12769, 103684, 1034289, 10278436, 102495376, 1026753849

Offset

0,1

Links

Table of n, a(n) for n=0..10.

Example

a(0) = 8 since 2^3 = 8, 3^2 = 9, and they share no digits in common.
The digit sets of 2^5 = 32: [2, 3] and 5^2 = 25: [2, 5] share exactly the digits [2] in common, so a(1) = 25.
The digit sets of 2^4 = 16: [1, 6] and 4^2 = 16: [1, 6] share exactly the digits [1, 6] in common, so a(2) = 16.
The digit sets of 2^36 = 68719476736: [1, 3, 4, 6, 7, 8, 9] and 36^2 = 1296: [1, 2, 6, 9] share exactly the digits [1, 6, 9] in common, so a(3) = 1296.
The digit sets of 2^52 = 4503599627370496: [0, 2, 3, 4, 5, 6, 7, 9] and 52^2 = 2704: [0, 2, 4, 7] share exactly the digits [0, 2, 4, 7] in common, so a(4) = 2704.
The digit sets of 2^113 = 10384593717069655257060992658440192: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] and 113^2 = 12769: [1, 2, 6, 7, 9] share exactly the digits [1, 2, 6, 7, 9] in common, so a(5) = 12769.
And no lesser numbers of the form a^b with 1 < a and 1 < b and a != b have this property.

Crossrefs

Sequence in context: A103954 A217012 A200838 * A302160 A122984 A254341

Adjacent sequences: A389846 A389847 A389848 * A389850 A389851 A389852

Keyword

nonn,base,fini,full

Author

Jean-Marc Rebert, Jan 26 2026

Extensions

a(0) prepended and a(6)-a(10) from Michael S. Branicky, Jan 26 2026

Status

approved