A244078 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_(j)*10^(j-1)}}’, where n’ is the arithmetic derivative of n (see example below).

13, 17, 23, 37, 43, 53, 67, 73, 83, 97, 131, 211, 241, 271, 311, 331, 431, 461, 541, 571, 631, 641, 661, 761, 811, 911, 941, 971, 1601, 3701, 5101, 5701, 6101, 6701, 8101, 9601, 13001, 16138, 18497, 19001, 22879, 24001, 54001, 69001, 93001, 97001, 99361, 270001

Offset

1,1

Comments

Mainly primes.

Links

Table of n, a(n) for n=1..48.

Example

If n = 16138, starting from the least significant digit, let us cut the number into the set {8, 38, 138, 6138}. We have:
8’ = 12;
38’ = 21;
138’ = 121;
6138’ = 7917.
Finally, 12 + 21 + 121 + 7917 = 16138’ = 8071.

Maple

with(numtheory); P:=proc(q) local a, c, k, n, p;
for n from 10 to q do
a:=0; k:=1; while (n mod 10^k)<n do c:=(n mod 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, A244077.

Sequence in context: A158072 A277689 A240894 * A126143 A145483 A349978

Adjacent sequences: A244075 A244076 A244077 * A244079 A244080 A244081

Keyword

nonn,base

Author

Paolo P. Lava, Jun 19 2014

Status

approved