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

1,1

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