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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)