A306208 Numbers x for which exists a number y such that x = Sum_{j=1..k}{y^(d_j) + (d_j)^y}, where d_j is one of the k digits of x.

10, 21, 100, 101, 111, 344, 1000, 1010, 1100, 3674, 10000, 10001, 11101, 100000, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101010, 101100, 101110, 101111, 110000, 110001, 110010, 110100, 110110, 110111, 111000, 111010, 111011, 111101, 427523, 1000000

Offset: 1

Author

Paolo P. Lava, Jan 29 2019

Keywords

• nonn
• base
• easy

Comments

Lowest values of y for zeroless numbers: e.g., x = 21, 344, 3674 -> y = 3, x = 427523 -> y = 6, x = 75818252 -> y = 8.

Examples

			x = 10 -> y = 8 because 8^1 + 8^0 + 1^8 + 0^8 = 10.
x = 21 -> y = 3 because 3^2 + 3^1 + 2^3 + 1^3 = 21.
x = 100 -> y = 97 because 97^1 + 97^0 + 97^0 + 1^97 + 0^97 + 0^97 = 100.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..147
• Paolo P. Lava, List of the first 147 numbers x along with their y

Crossrefs

Cf. A258484.

Programs

Maple

P:=proc(q) local a,b,j,k,n; for n from 1 to q do
a:=convert(n,base,10); for k from 1 to q do
b:=add(j^k+k^j,j=a); if b>n then break; else
if n=b then print(n); fi; fi; od; od; end: P(10^9);