A325323 -id:A325323 - cp's OEIS frontend

A325322 Palindromes in base 10 that are Brazilian.

7, 8, 22, 33, 44, 55, 66, 77, 88, 99, 111, 121, 141, 161, 171, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 323, 333, 343, 363, 393, 404, 414, 424, 434, 444, 454, 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

Offset: 1

Bernard Schott, Apr 20 2019

Among the terms of this sequence, there are (not exhaustive):
- the even palindromes >= 8,
- the palindromes >= 55 that end with 5,
- the palindromes >= 22 with an even number of digits for they are divisible by 11, and also,
- the palindromes that are Brazilian primes such as 7, 757, 30103, ...

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A002113 and A125134.
Complement of A325323 with respect to A002113.
Cf. A288068 (subsequence).

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 *)

isb(n) = for(b=2, n-2, my(d=digits(n, b)); if(vecmin(d)==vecmax(d), return(1))); \\ A125134
isp(n) = my(d=digits(n)); d == Vecrev(d); \\ A002113
isok(n) = isb(n) && isp(n); \\ Michel Marcus, Apr 22 2019

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A325322 Palindromes in base 10 that are Brazilian.

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