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).

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

Cf. A000203, A240895-A240902.

Sequence in context: A227916 A158072 A277689 * A244078 A126143 A145483

Adjacent sequences: A240891 A240892 A240893 * A240895 A240896 A240897

Keyword

nonn,base

Author

Paolo P. Lava, Apr 14 2014

Status

approved