A240899 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)})} (see example below).

11, 13, 17, 19, 143, 473, 419645, 17913329, 27479459, 4113856765, 9696564647, 17207135705, 21202976255

Offset

1,1

Comments

a(14) > 3*10^10. - Giovanni Resta, Apr 16 2014

Links

Table of n, a(n) for n=1..13.

Example

If n = 473, starting from the most significant digit, let us cut the number into the set 4, 47. We have:
sigma(4) = 7;
sigma(47) = 48
and 7 + 48 = 55 = sigma(473) - 473.

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)); k:=k+1; od;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000203, A240894-A240898, A240900, A240902.

Sequence in context: A356987 A327348 A327349 * A090149 A337834 A089691

Adjacent sequences: A240896 A240897 A240898 * A240900 A240901 A240902

Keyword

nonn,base,more

Author

Paolo P. Lava, Apr 14 2014

Extensions

a(7)-a(13) from Giovanni Resta, Apr 16 2014

Status

approved