cp's OEIS Frontend

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.

%I A306208 #23 Feb 06 2019 13:06:58
%S A306208 10,21,100,101,111,344,1000,1010,1100,3674,10000,10001,11101,100000,
%T A306208 100010,100011,100100,100101,100110,101000,101001,101010,101100,
%U A306208 101110,101111,110000,110001,110010,110100,110110,110111,111000,111010,111011,111101,427523,1000000
%N 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.
%C A306208 Lowest values of y for zeroless numbers: e.g., x = 21, 344, 3674 -> y = 3, x = 427523 -> y = 6, x = 75818252 -> y = 8.
%H A306208 Paolo P. Lava, <a href="/A306208/b306208.txt">Table of n, a(n) for n = 1..147</a>
%H A306208 Paolo P. Lava, <a href="/A306208/a306208.txt">List of the first 147 numbers x along with their y</a>
%e A306208 x = 10 -> y = 8 because 8^1 + 8^0 + 1^8 + 0^8 = 10.
%e A306208 x = 21 -> y = 3 because 3^2 + 3^1 + 2^3 + 1^3 = 21.
%e A306208 x = 100 -> y = 97 because 97^1 + 97^0 + 97^0 + 1^97 + 0^97 + 0^97 = 100.
%p A306208 P:=proc(q) local a,b,j,k,n; for n from 1 to q do
%p A306208 a:=convert(n,base,10); for k from 1 to q do
%p A306208 b:=add(j^k+k^j,j=a); if b>n then break; else
%p A306208 if n=b then print(n); fi; fi; od; od; end: P(10^9);
%Y A306208 Cf. A258484.
%K A306208 nonn,base,easy
%O A306208 1,1
%A A306208 _Paolo P. Lava_, Jan 29 2019