login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Nonprime base-10 palindromes whose arithmetic derivative is a base-10 palindrome.
0

%I #6 May 25 2023 07:52:16

%S 0,1,4,6,9,121,222,717,989,1331,10201,13231,15251,15751,15851,18281,

%T 19291,28882,28982,31613,34043,35653,37073,37673,37873,38383,38683,

%U 40304,41814,50405,97079,98789,99899,536635,913319,980089,1030301,1115111,1226221,1336331,1794971,2630362,2882882,3303033

%N Nonprime base-10 palindromes whose arithmetic derivative is a base-10 palindrome.

%C Nonprime members k of A002113 such that A003415(k) is also in A002113.

%C A003415(p) = 1 is a palindrome for all primes p. It seems that most members of A363246 are primes.

%e a(7) = 222 is a term because it is a palindrome, is not prime, and its arithmetic derivative 191 is a palindrome.

%p ader:= proc(n) local t;

%p n*add(t[2]/t[1],t=ifactors(n)[2])

%p end proc:

%p rev:= proc(n) local L,i;

%p L:= convert(n,base,10);

%p add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p palis:= proc(d) local x,y;

%p if d::even then seq(10^(d/2)*x+rev(x),x=10^(d/2-1)..10^(d/2)-1)

%p 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 fi

%p end proc:

%p palis(1):= $0..9:

%p filter:= proc(n) local d;

%p if isprime(n) then return false fi;

%p d:= ader(n);

%p d = rev(d)

%p end proc:

%p select(filter, [seq(palis(i),i=1..7)]);

%Y Cf. A002113, A003415. Complement of A002385 in A363246.

%K nonn,base

%O 1,3

%A _Robert Israel_, May 23 2023