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%I A363248 #6 May 25 2023 07:52:16
%S A363248 0,1,4,6,9,121,222,717,989,1331,10201,13231,15251,15751,15851,18281,
%T A363248 19291,28882,28982,31613,34043,35653,37073,37673,37873,38383,38683,
%U A363248 40304,41814,50405,97079,98789,99899,536635,913319,980089,1030301,1115111,1226221,1336331,1794971,2630362,2882882,3303033
%N A363248 Nonprime base-10 palindromes whose arithmetic derivative is a base-10 palindrome.
%C A363248 Nonprime members k of A002113 such that A003415(k) is also in A002113.
%C A363248 A003415(p) = 1 is a palindrome for all primes p. It seems that most members of A363246 are primes.
%e A363248 a(7) = 222 is a term because it is a palindrome, is not prime, and its arithmetic derivative 191 is a palindrome.
%p A363248 ader:= proc(n) local t;
%p A363248   n*add(t[2]/t[1],t=ifactors(n)[2])
%p A363248 end proc:
%p A363248 rev:= proc(n) local L,i;
%p A363248   L:= convert(n,base,10);
%p A363248   add(L[-i]*10^(i-1),i=1..nops(L))
%p A363248 end proc:
%p A363248 palis:= proc(d) local x,y;
%p A363248   if d::even then seq(10^(d/2)*x+rev(x),x=10^(d/2-1)..10^(d/2)-1)
%p A363248   else seq(seq(10^((d+1)/2)*x+10^((d-1)/2)*y+rev(x), y=0..9),x=10^((d-3)/2) ..10^((d-1)/2)-1)
%p A363248   fi
%p A363248 end proc:
%p A363248 palis(1):= $0..9:
%p A363248 filter:= proc(n) local d;
%p A363248     if isprime(n) then return false fi;
%p A363248     d:= ader(n);
%p A363248   d = rev(d)
%p A363248 end proc:
%p A363248 select(filter, [seq(palis(i),i=1..7)]);
%Y A363248 Cf. A002113, A003415.  Complement of A002385 in A363246.
%K A363248 nonn,base
%O A363248 1,3
%A A363248 _Robert Israel_, May 23 2023

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