A263024 Digits of composite n end in n', where n' is the arithmetic derivative of n.

19131, 1909131, 14222539, 17654359, 51783947, 59724191, 628025227, 745058551, 938403959, 1637154151, 1834714151, 2369329447, 3871912651, 19090909131, 24934617431, 26450868967, 28346927071, 29730856667, 47968127851, 48264490991, 51096197231, 55762015591, 83490323671

Offset

1,1

Comments

Primes are not considered because any prime ending in 1 would be part of the sequence.

Also numbers of the form n = p^p, with p prime, for which n = n', are not considered.

Up to 10^11 all the terms are the product of 3 distinct primes. If p = (21+100^k)/11 is a prime larger than 11, then the number 3*7*p belongs to this sequence. This happens for k = 2, 3, 5, 52, 1923, 2879,... - Giovanni Resta, May 28 2016

Links

Table of n, a(n) for n=1..23.

Example

19131' = 9131, 1909131' = 909131, 14222539' = 222539, 17654359' = 654359, 51783947' = 783947, 59724191' = 724191.

Maple

with(numtheory): P:=proc(q) local a, b, n, p;
for n from 1 to q do if not isprime(n) then
a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
if a<n then b:=ilog10(a)+1; if a=(n mod 10^b) then print(n);
fi; fi; fi; od; end: P(10^9);

Crossrefs

Cf. A003415, A249540.

Sequence in context: A251041 A234724 A237554 * A367650 A015302 A249106

Adjacent sequences: A263021 A263022 A263023 * A263025 A263026 A263027

Keyword

nonn,base

Author

Paolo P. Lava, Oct 08 2015

Extensions

a(7)-a(12) from Altug Alkan, Oct 08 2015

a(13)-a(23) from Giovanni Resta, May 28 2016

Status

approved