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A244077 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 n’ = Sum_{i=1..k-1}{Sum_{j=1..i}{d_(k-j+1)*10^(i-j)}}’, where n’ is the arithmetic derivative of n (see example below). 1
23, 29, 31, 37, 53, 59, 71, 73, 79, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 6437, 8339, 14473, 60827, 95611, 107813 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From 23 to 199 only primes, then composites.

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

If n = 14473, starting from the most significant digit, let us cut the number into the set {1, 14, 144, 1447}. We have:

1’ = 0;

14’ = 9;

144’ = 384;

1447’ = 1.

Finally, 0 + 9 + 384 + 1 = 14473’ = 394.

MAPLE

with(numtheory); P:=proc(q) local a, c, k, n, p;

for n from 10 to q do

a:=0; k:=1; while trunc(n/10^k)>0 do c:=trunc(n/10^k);

a:=a+c*add(op(2, p)/op(1, p), p=ifactors(c)[2]); k:=k+1; od;

if a=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]) then print(n);

fi; od; end: P(10^10);

CROSSREFS

Cf. A003415, A240894-A240903, A241207, A241502, A241503, A244068, A244069, A244078.

Sequence in context: A155913 A227919 A240898 * A277206 A214754 A153631

Adjacent sequences:  A244074 A244075 A244076 * A244078 A244079 A244080

KEYWORD

nonn,more,base

AUTHOR

Paolo P. Lava, Jun 19 2014

STATUS

approved

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Last modified August 25 05:45 EDT 2019. Contains 326323 sequences. (Running on oeis4.)