A363248 Nonprime 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

Offset

1,3

Comments

Nonprime 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.

Links

Table of n, a(n) for n=1..44.

Example

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

Maple

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)]);

Crossrefs

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

Sequence in context: A245044 A104389 A115655 * A084350 A028279 A114743

Adjacent sequences: A363245 A363246 A363247 * A363249 A363250 A363251

Keyword

nonn,base

Author

Robert Israel, May 23 2023

Status

approved