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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)