perplexus.info :: Numbers : Narcissistic minus 1: Cerossistic

Narcissistic minus 1: Cerossistic (Posted on 2023-01-05)

A Narcissistic number is a positive integer that equals the sum of M-th powers of their digits when the number is M-digit long.

153 is a Narcissistic number, since: 1³+5³+3³=153.
Sloane's A005188 has an article on this, in which inter-alia it is mentioned that the sequence of Narcissistic numbers terminates at the 88th term.

A Cerossistic number is a base ten M-digit long positive integer which is equal to the sum of M-th powers of one less than each of the digits.

For example, if we check for 371 we find that:
2³+6³+0³ = 224, which is NOT equal to 371.

Determine the smallest Cerossistic number.

Note: No Cerossistic number can admit of the digit zero.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

computer solution

| Comment 2 of 4 |

for i=1:100000000

n=char(string(i)); t=0;

p=length(n);

t=sum((n-49).^p);

if t==i

disp(i);

end

finds

so the smallest is 26.

The prohibition on zero was not programmed into the algorithm, explaining the inclusion of 134068. It's included on the list as

0^6 + 2^6 + 3^6 + (-1)^6 +5^6 + 7^6 = 134068

and likewise for 10875747, but this doesn't affect the fact that 26 is the smallest.

Posted by Charlie on 2023-01-05 10:14:00

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