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

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;
sigma(2346) - 2346 = 2838;
sigma(23463) - 23463 = 14937
and 1 + 1 + 312 + 2838 + 14937 = 18089 = sigma(234631) - 234631.

Maple

with(numtheory); P:=proc(q) local a, k, n;
for n from 2 to q do a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+sigma(trunc(n/10^k))-trunc(n/10^k); k:=k+1; od;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000203, A240894-A240897, A240899-A240902.

Sequence in context: A078500 A155913 A227919 * A244077 A277206 A214754

Adjacent sequences: A240895 A240896 A240897 * A240899 A240900 A240901

Keyword

nonn,base

Author

Paolo P. Lava, Apr 14 2014

Extensions

a(23)-a(37) from Giovanni Resta, Apr 16 2014

Status

approved