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).

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

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 A344375

Adjacent sequences: A244074 A244075 A244076 * A244078 A244079 A244080

Keyword

nonn,more,base

Author

Paolo P. Lava, Jun 19 2014

Status

approved