cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A325322 Palindromes in base 10 that are Brazilian.

This page as a plain text file.
%I A325322 #35 Apr 14 2021 05:25:07
%S A325322 7,8,22,33,44,55,66,77,88,99,111,121,141,161,171,202,212,222,232,242,
%T A325322 252,262,272,282,292,303,323,333,343,363,393,404,414,424,434,444,454,
%U A325322 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 A325322 Palindromes in base 10 that are Brazilian.
%C A325322 Among the terms of this sequence, there are (not exhaustive):
%C A325322 - the even palindromes >= 8,
%C A325322 - the palindromes >= 55 that end with 5,
%C A325322 - the palindromes >= 22 with an even number of digits for they are divisible by 11, and also,
%C A325322 - the palindromes that are Brazilian primes such as 7, 757, 30103, ...
%H A325322 Amiram Eldar, <a href="/A325322/b325322.txt">Table of n, a(n) for n = 1..10000</a>
%e A325322 141 = (33)_46 is a palindrome that is Brazilian.
%t A325322 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 A325322 (PARI) isb(n) = for(b=2, n-2, my(d=digits(n, b)); if(vecmin(d)==vecmax(d), return(1))); \\ A125134
%o A325322 isp(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113
%o A325322 isok(n) = isb(n) && isp(n); \\ _Michel Marcus_, Apr 22 2019
%Y A325322 Intersection of A002113 and A125134.
%Y A325322 Complement of A325323 with respect to A002113.
%Y A325322 Cf. A288068 (subsequence).
%K A325322 nonn,base
%O A325322 1,1
%A A325322 _Bernard Schott_, Apr 20 2019