

A244144


Alternating sum of digits of n^n.


3



1, 4, 5, 3, 1, 5, 5, 5, 5, 1, 11, 10, 8, 4, 21, 38, 8, 2, 7, 1, 1, 0, 10, 5, 23, 26, 3, 7, 19, 23, 24, 23, 11, 56, 10, 36, 5, 37, 24, 32, 8, 15, 1, 33, 10, 20, 20, 35, 31, 23, 18, 24, 14, 34, 0, 1, 40, 16, 14, 21, 6, 27, 17, 5, 32, 11, 12, 41, 59, 23, 38, 52, 42, 29, 21, 12, 0, 1, 39, 1, 7, 19, 7, 25, 34
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The alternating sum of the digits of n^n is the sum obtained by alternately adding and subtracting the digits of n^n from left to right. For example, 4^4 = 256, therefore the alternating sum = 2  5 + 6 = 3. 7^7 = 823543, alternating sum = 8  2 + 3  5 + 4  3 = 5.


LINKS



EXAMPLE

If the function f(x) alternately adds and subtracts the digits of x from left to right, then:
a(1) = f(1^1) = f(1) = 1.
a(2) = f(2^2) = f(4) = 4.
a(3) = f(3^3) = f(27) = 2  7 = 5.
a(4) = f(4^4) = f(256) = 2  5 + 6 = 3.
a(9) = f(9^9) = f(387420489) = 3  8 + 7  4 + 2  0 + 4  8 + 9 = 5.


MAPLE

a:= n> (s>add(parse(s[i])*(1)^i, i=1..length(s)))(""(n^n)):


MATHEMATICA

f[n_] := Block[ {d = Reverse[ IntegerDigits[ n]], k = l = 1, s = 0}, l = Length[d]; While[ k <= l, s = s  (1)^k*d[[k]]; k++ ]; Return[s]]; Table[ f[n^n], {n, 1, 100} ] \\ Minor adaptation from program for A065796.


CROSSREFS



KEYWORD

sign,base,less


AUTHOR



STATUS

approved



