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

1,1

Comments

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, ...

Links

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

Example

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

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

Intersection of A002113 and A125134.

Complement of A325323 with respect to A002113.

Cf. A288068 (subsequence).

Sequence in context: A132899 A051175 A322651 * A288068 A058537 A002362

Adjacent sequences: A325319 A325320 A325321 * A325323 A325324 A325325

Keyword

nonn,base

Author

Bernard Schott, Apr 20 2019

Status

approved