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proposed

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

Non-prime Nonprime members k of A002113 such that A003415(k) is also in A002113.

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proposed

allocated for Robert IsraelNon-prime base-10 palindromes whose arithmetic derivative is a base-10 palindrome.

0, 1, 4, 6, 9, 121, 222, 717, 989, 1331, 10201, 13231, 15251, 15751, 15851, 18281, 19291, 28882, 28982, 31613, 34043, 35653, 37073, 37673, 37873, 38383, 38683, 40304, 41814, 50405, 97079, 98789, 99899, 536635, 913319, 980089, 1030301, 1115111, 1226221, 1336331, 1794971, 2630362, 2882882, 3303033

1,3

Non-prime members k of A002113 such that A003415(k) is also in A002113.

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

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

ader:= proc(n) local t;

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

end proc:

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

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

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

end proc:

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

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

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)

fi

end proc:

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

filter:= proc(n) local d;

if isprime(n) then return false fi;

d:= ader(n);

d = rev(d)

end proc:

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

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

allocated

nonn,base

Robert Israel, May 23 2023

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allocated for Robert Israel

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