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%I #7 Mar 27 2014 04:49:04
%S 169,209,1027,1219,1339,1929,1966,2581,11569,17251,17845,18419,26093,
%T 59987,98699,106159,107629,115069,131179,137533,147019,150071,151519,
%U 155471,168505,186911,188297,207413,217999,221027,230183,231437,276413,298891,368813,400921
%N Composite numbers n such that if n = a U b (where U denotes concatenation) then a’ + b’ = n’, where a’, b’ and n’ are the arithmetic derivatives of a, b and n.
%H Paolo P. Lava, <a href="/A239724/b239724.txt">Table of n, a(n) for n = 1..100</a>
%e The arithmetic derivative of 2581 is 118. Consider 2581 = 25 U 81. The arithmetic derivative of 25 is 10 and of 81 is 108. Therefore we have 10 + 108 = 118.
%p with(numtheory);T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
%p P:=proc(q) local a, b, c, d, f, g,i, n,p; for n from 1 to q do if not isprime(n) then b:=T(n);
%p a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]); for i from 1 to b-1 do c:=trunc(n/10^i); d:=n-c*10^i;
%p f:=c*add(op(2,p)/op(1,p),p=ifactors(c)[2]); g:=d*add(op(2,p)/op(1,p),p=ifactors(d)[2]);
%p if f+g=a then print(n); break; fi; od; fi; od; end: P(10^9);
%Y Cf. A003415.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Mar 25 2014
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