

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.


1



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
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OFFSET

1,1


COMMENTS

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


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


EXAMPLE

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.


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);


CROSSREFS

Cf. A258484.
Sequence in context: A215574 A146083 A321722 * A001739 A072805 A119033
Adjacent sequences: A306205 A306206 A306207 * A306209 A306210 A306211


KEYWORD

nonn,base,easy


AUTHOR

Paolo P. Lava, Jan 29 2019


STATUS

approved



