A363246 Base-10 palindromes whose arithmetic derivative is also a base-10 palindrome.

0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 101, 121, 131, 151, 181, 191, 222, 313, 353, 373, 383, 717, 727, 757, 787, 797, 919, 929, 989, 1331, 10201, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13231, 13331, 13831, 13931, 14341, 14741, 15251, 15451, 15551, 15751, 15851, 16061, 16361, 16561

Offset

1,3

Comments

Members k of A002113 such that A003415(k) is also in A002113.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(12) = 121 is a term because 121 is a palindrome and its arithmetic derivative 22 is also 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:
filter:= proc(n) local d;
    if n <> rev(n) then return false fi;
    d:= ader(n);
  d = rev(d)
end proc:
select(filter, [$0..20000]);

Prog

(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
ispal(q) = my(d=digits(q)); d == Vecrev(d); \\ A002113
isok(q) = ispal(q) && ispal(ad(q)); \\ Michel Marcus, May 25 2023

Crossrefs

Cf. A002113, A003415. Includes A002385.

Sequence in context: A263362 A336733 A072966 * A245761 A371248 A059759

Adjacent sequences: A363243 A363244 A363245 * A363247 A363248 A363249

Keyword

nonn,base

Author

Robert Israel, May 23 2023

Status

approved