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
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);
Comments