A030147 Palindromes in which parity of digits alternates.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 121, 141, 161, 181, 212, 232, 252, 272, 292, 303, 323, 343, 363, 383, 414, 434, 454, 474, 494, 505, 525, 545, 565, 585, 616, 636, 656, 676, 696, 707, 727, 747, 767, 787, 818, 838, 858, 878, 898, 909, 929, 949

Offset

1,3

Comments

All terms have an odd number of digits. - Alonso del Arte, Jan 31 2020

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to palindromes

Formula

A136522(a(n)) * A228710(a(n)) = 1. - Reinhard Zumkeller, Aug 31 2013

Mathematica

palQ[n_, b_:10] := (IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]); alternParQ[n_, b_:10] := (Union[BlockMap[Xor @@ # &, OddQ[IntegerDigits[n, b]], 2, 1]] == {True}); Join[Range[0, 9], Select[Range[1000], palQ[#] && alternParQ[#] &]] (* Alonso del Arte, Feb 02 2020 *)
Join[Range[0, 9], Select[Range[100000], PalindromeQ[#]&&Union[Total/@Partition[Boole[ EvenQ[ IntegerDigits[ #]]], 2, 1]] =={1}&]] (* Harvey P. Dale, Jul 04 2023 *)

Prog

(Haskell)
a030147 n = a030147_list !! (n-1)
a030147_list = filter ((== 1) . a228710) a002113_list
-- Reinhard Zumkeller, Aug 31 2013
(Scala) def isPal(n: Int) = (n.toString == n.toString.reverse)
def alternsPar(n: Int): Boolean = {
  val dPars = Integer.toString(n).toList.map(_ % 2 == 0)
  val scanPars = (dPars zip dPars.tail).map{ case (x, y) => x ^ y }
  scanPars.toSet == Set(true)
}
(0 to 9) ++: (10 to 999).filter(isPal).filter(alternsPar) // Alonso del Arte, Feb 02 2020

Crossrefs

Intersection of A002113 and A030141.

Subsequence of A001633.

Cf. A030143, A030144, A030152.

Sequence in context: A083851 A071275 A050783 * A207954 A193412 A266139

Adjacent sequences: A030144 A030145 A030146 * A030148 A030149 A030150

Keyword

nonn,base

Author

Patrick De Geest

Status

approved