A325322 - OEIS

%I #35 Apr 14 2021 05:25:07

%S 7,8,22,33,44,55,66,77,88,99,111,121,141,161,171,202,212,222,232,242,

%T 252,262,272,282,292,303,323,333,343,363,393,404,414,424,434,444,454,

%U 464,474,484,494,505,515,525,535,545,555,565,575,585,595,606,616,626,636,646,656,666,676,686,696,707,717,737

%N Palindromes in base 10 that are Brazilian.

%C Among the terms of this sequence, there are (not exhaustive):

%C - the even palindromes >= 8,

%C - the palindromes >= 55 that end with 5,

%C - the palindromes >= 22 with an even number of digits for they are divisible by 11, and also,

%C - the palindromes that are Brazilian primes such as 7, 757, 30103, ...

%H Amiram Eldar, <a href="/A325322/b325322.txt">Table of n, a(n) for n = 1..10000</a>

%e 141 = (33)_46 is a palindrome that is Brazilian.

%t brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length @ Union[IntegerDigits[n, b]] > 1, b++]; b < n - 1]; Select[Range[1000], PalindromeQ[#] && brazQ[#] &] (* _Amiram Eldar_, Apr 14 2021 *)

%o (PARI) isb(n) = for(b=2, n-2, my(d=digits(n, b)); if(vecmin(d)==vecmax(d), return(1))); \\ A125134

%o isp(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113

%o isok(n) = isb(n) && isp(n); \\ _Michel Marcus_, Apr 22 2019

%Y Intersection of A002113 and A125134.

%Y Complement of A325323 with respect to A002113.

%Y Cf. A288068 (subsequence).

%K nonn,base

%O 1,1

%A _Bernard Schott_, Apr 20 2019