|
|
A240894
|
|
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_(j)*10^(j-1)}) - Sum_{j=1..i}{d_(j)*10^(j-1)}} (see example below).
|
|
17
|
|
|
13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 131, 211, 241, 271, 311, 331, 431, 461, 541, 571, 631, 641, 661, 761, 811, 899, 911, 941, 971, 1601, 3701, 5101, 5701, 6101, 6701, 8101, 9601, 13001, 19001, 24001, 54001, 69001, 93001, 97001, 102737, 194357, 217267
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Mainly primes. The first composite numbers in the sequence are 899, 102737, 194357, 217267, 377149, etc.
|
|
LINKS
|
|
|
EXAMPLE
|
If n = 194357, starting from the least significant digit, let us cut the number into the set 7, 57, 357, 4357, 94357. We have:
sigma(7) - 7 = 1;
sigma(57) - 57 = 23;
sigma(357) - 357 = 219;
sigma(4357) - 4357 = 1;
sigma(94357) - 94357 = 759
and 1 + 23 + 219 + 1 + 759 = 1003 = sigma(194357) - 194357.
|
|
MAPLE
|
with(numtheory); P:=proc(q) local a, k, n;
for n from 2 to q do a:=0; k:=1; while (n mod 10^k)<n do
a:=a+sigma(n mod 10^k)-(n mod 10^k); k:=k+1; od;
if sigma(n)-n=a then print(n); fi; od; end: P(10^9);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|