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%I #26 Mar 22 2019 12:09:54
%S 19131,1909131,14222539,17654359,51783947,59724191,628025227,
%T 745058551,938403959,1637154151,1834714151,2369329447,3871912651,
%U 19090909131,24934617431,26450868967,28346927071,29730856667,47968127851,48264490991,51096197231,55762015591,83490323671
%N Digits of composite n end in n', where n' is the arithmetic derivative of n.
%C Primes are not considered because any prime ending in 1 would be part of the sequence.
%C Also numbers of the form n = p^p, with p prime, for which n = n', are not considered.
%C 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
%e 19131' = 9131, 1909131' = 909131, 14222539' = 222539, 17654359' = 654359, 51783947' = 783947, 59724191' = 724191.
%p with(numtheory): P:=proc(q) local a,b,n,p;
%p for n from 1 to q do if not isprime(n) then
%p a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
%p if a<n then b:=ilog10(a)+1; if a=(n mod 10^b) then print(n);
%p fi; fi; fi; od; end: P(10^9);
%Y Cf. A003415, A249540.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Oct 08 2015
%E a(7)-a(12) from _Altug Alkan_, Oct 08 2015
%E a(13)-a(23) from _Giovanni Resta_, May 28 2016