Voozh

A240898

Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that sigma(n) - n = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)}) - Sum_{j=1..i}{d_(k-j+1)*10^(i-j)}} (see example below).

23, 29, 31, 37, 53, 59, 71, 73, 79, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 5627, 109667, 234631, 470383, 785833, 884539, 7004885, 27794549, 134035373, 161827399, 168838613, 1180754999, 1237998833, 1633413359, 2827151629, 3283714933, 5356159891, 13356724387

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OFFSET

1,1

COMMENTS

Terms a(1)-a(19) are primes, terms a(20)-a(37) are composite.

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

If n = 234631, starting from the most significant digit, let us cut the number into the set 2, 23, 234, 2346, 23463. We have:

sigma(2) - 2 = 1;

sigma(23) - 23 = 1;

sigma(234) - 234 = 312;