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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A125262

Adjacent sequences:  A244075 A244076 A244077 * A244079 A244080 A244081

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Jun 19 2014

STATUS

approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)