login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Palindromes in base 10 that are Brazilian.
2

%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