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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
OFFSET
1,1
COMMENTS
Mainly primes. The first composite numbers in the sequence are 899, 102737, 194357, 217267, 377149, etc.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..135 (terms < 10^10)
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
Paolo P. Lava, Apr 14 2014
STATUS
approved