cp's OEIS Frontend

A276354 Palindromes n > 0 such that the sum of all distinct permutations of the digits of n is also a palindrome.

%I A276354 #37 Feb 01 2017 10:27:03
%S A276354 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,111,121,131,141,151,
%T A276354 161,171,191,202,212,222,232,242,252,272,303,313,323,333,353,404,414,
%U A276354 434,444,515,555,666,777,787,868,888,949,999,1001,1111,1221,2002,2112,2222,2992
%N A276354 Palindromes n > 0 such that the sum of all distinct permutations of the digits of n is also a palindrome.
%C A276354 Values of A002113(n) such that A045876(A002113(n)) is in A002113 (n > 0).
%C A276354 If n has a zero digit then the permutations starting with 0 are included in the sum (i.e., 0010 is taken to be 10, 01 is taken to be 1, etc.).
%C A276354 A010785(n) is an obvious term of this sequence for all n > 0.
%H A276354 Indranil Ghosh, <a href="/A276354/b276354.txt">Table of n, a(n) for n = 1..385</a>
%e A276354 101 is a term because 11 + 101 + 110 = 222 is also a palindrome.
%e A276354 232 is a term because 223 + 232 + 322 = 777 is also a palindrome.
%e A276354 2002 is a term because 22 + 202 + 220 + 2002 + 2020 + 2200 = 6666 is also a palindrome.
%o A276354 (PARI) A047726(n) = n=eval(Vec(Str(n))); (#n)!/prod(i=0, 9, sum(j=1, #n, n[j]==i)!);
%o A276354 A055642(n) = #Str(n);
%o A276354 A007953(n) = sumdigits(n);
%o A276354 A045876(n) = ((10^A055642(n)-1)/9)*(A047726(n)*A007953(n)/A055642(n));
%o A276354 isA002113(n) = n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1;
%o A276354 lista(nn) = for(n=1, nn, if(isA002113(n) && isA002113(A045876(n)), print1(n", ")));
%Y A276354 Cf. A002113, A007953, A010785, A045876, A047726, A055642.
%K A276354 nonn,easy,base
%O A276354 1,2
%A A276354 _Altug Alkan_, Sep 05 2016