A328332 -id:A328332

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A029950

Odd palindromes.

+10
6

1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 909, 919, 929, 939, 949

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

There are more odd palindromes (A328332) less than 10^K than even palindromes (A328333) because odd palindromes begin with 1, 3, 5, 7 or 9 while even palindromes begin only with 2, 4, 6 or 8. - Bernard Schott, Oct 24 2019

LINKS

Philip Mizzi, Table of n, a(n) for n = 1..7110 (terms up to 20000000).

P. De Geest, World!Of Numbers

Index entries for sequences related to palindromes

MATHEMATICA

palindromicQ[n_, b_:10]:=TrueQ[IntegerDigits[n, b]==Reverse[IntegerDigits[n, b]]]; Select[Range[1, 10^4, 2], palindromicQ[#]&&Plus@@Drop[DigitCount[#], {1, 10, 1}]==0&] (* Vincenzo Librandi, Feb 07 2014 *)

Select[Range[1, 949, 2], PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 15 2017 *)

PROG

(PARI) lista(nn) = {forstep(n=1, nn, 2, if (is_A002113(n), print1(n, ", "))); } \\ Michel Marcus, Feb 06 2014

CROSSREFS

Subsequence of A002113.

Cf. A029951 (even palindromes), A328332, A328333.

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

EXTENSIONS

Offset set to 1 and more terms from Michel Marcus, Feb 06 2014

STATUS

approved

A328333

Expansion of (1 + 4*x - 6*x^2) / ((1 - x) * (1 - 10*x^2)).

+10
2

1, 5, 9, 49, 89, 489, 889, 4889, 8889, 48889, 88889, 488889, 888889, 4888889, 8888889, 48888889, 88888889, 488888889, 888888889, 4888888889, 8888888889, 48888888889, 88888888889, 488888888889, 888888888889, 4888888888889, 8888888888889, 48888888888889, 88888888888889

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Number of even palindromes < 10^n.

LINKS

Table of n, a(n) for n=0..28.

Eric Weisstein's World of Mathematics, Palindromic Number

Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

MATHEMATICA

nmax = 28; CoefficientList[Series[(1 + 4 x - 6 x^2)/((1 - x) (1 - 10 x^2)), {x, 0, nmax}], x]

LinearRecurrence[{1, 10, -10}, {1, 5, 9}, 29]