A029951 -id:A029951 - cp's OEIS frontend

A083852 Decimal palindromes that are multiples of 11.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 121, 242, 363, 484, 616, 737, 858, 979, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443, 3553, 3663, 3773, 3883, 3993, 4004

Offset: 1

Reinhard Zumkeller, May 06 2003

A083850(a(n))>0; palindromes with even length are terms.

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..1908

Intersection of A002113 and A008593.

Cf. A029951, A045638, A045639, A043040, A043041, A045642, A045643, A045644, A083851.

Select[Range[0, 5500, 11], PalindromeQ] (* Paolo Xausa, Jul 07 2025 *)

forstep(k=0, 10^5, 11, d=digits(k); d==Vecrev(d) && print1(k, ", ")) \\ Jeppe Stig Nielsen, May 08 2020

A043040 Numbers that are palindromic and divisible by 5.

Original entry on oeis.org

0, 5, 55, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 5005, 5115, 5225, 5335, 5445, 5555, 5665, 5775, 5885, 5995, 50005, 50105, 50205, 50305, 50405, 50505, 50605, 50705, 50805, 50905, 51015, 51115, 51215, 51315, 51415, 51515, 51615, 51715, 51815, 51915

Offset: 1

Clark Kimberling

Or, 0 and numbers that are palindromic and begin with 5.

Jaroslav Krizek, Table of n, a(n) for n = 1..2223

Intersection of A002113 and A008587.

Cf. A029951, A045638, A045639, A045641, A045642, A045643, A045644, A083852.

palQ[n_Integer, base_Integer] := Module[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]];
Join[{0},Select[Range[5,100000,5], IntegerDigits[#][[1]] == 5 && palQ[#, 10] &]] (* T. D. Noe, Mar 12 2013 *)
Select[5*Range[0,11000],IntegerDigits[#]==Reverse[IntegerDigits[#]]&] (* Harvey P. Dale, Nov 29 2015 *)

Edited to include a(1) = 0 by Paolo Xausa, Jul 07 2025

A045642 Palindromic and divisible by 7.

Original entry on oeis.org

0, 7, 77, 161, 252, 343, 434, 525, 595, 616, 686, 707, 777, 868, 959, 1001, 1771, 2002, 2772, 3003, 3773, 4004, 4774, 5005, 5775, 6006, 6776, 7007, 7777, 8008, 8778, 9009, 9779, 10101, 10801, 11011, 11711, 12621, 13531, 14441, 15351, 16261, 16961

Offset: 1

Jeff Burch

Paolo Xausa, Table of n, a(n) for n = 1..2000

Intersection of A002113 and A008589.

Cf. A029951, A045638, A045639, A043040, A045641, A045643, A045644, A083852.

Select[Range[0, 21000, 7], PalindromeQ] (* Paolo Xausa, Jul 06 2025 *)

a(1) = 0 prepended by Paolo Xausa, Jul 07 2025

A045638 Palindromic and divisible by 3.

Original entry on oeis.org

0, 3, 6, 9, 33, 66, 99, 111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999, 1221, 1551, 1881, 2112, 2442, 2772, 3003, 3333, 3663, 3993, 4224, 4554, 4884, 5115

Offset: 1

Jeff Burch

Harvey P. Dale, Table of n, a(n) for n = 1..2001

Intersection of A002113 and A008585.

Cf. A029951, A045639, A043040, A045641, A045642, A045643, A045644, A083852.

Select[Range[0,5500,3],PalindromeQ] (* Harvey P. Dale, Apr 14 2023 *)

Edited to include a(1) = 0 by Paolo Xausa, Jul 07 2025

A045639 Palindromic and divisible by 4.

Original entry on oeis.org

0, 4, 8, 44, 88, 212, 232, 252, 272, 292, 404, 424, 444, 464, 484, 616, 636, 656, 676, 696, 808, 828, 848, 868, 888, 2112, 2332, 2552, 2772, 2992, 4004, 4224, 4444, 4664, 4884, 6116, 6336, 6556, 6776, 6996, 8008, 8228, 8448, 8668, 8888, 21012, 21112, 21212

Offset: 1

Jeff Burch

Paolo Xausa, Table of n, a(n) for n = 1..3000

Intersection of A002113 and A008586.

Cf. A029951, A045638, A043040, A045641, A045642, A045643, A045644, A083852.

palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; Select[4*Range[0, 6000],palQ]  (* Harvey P. Dale, Jan 30 2011 *)

Edited to include a(1) = 0 by Paolo Xausa, Jul 07 2025

A045643 Palindromic and divisible by 8.

Original entry on oeis.org

0, 8, 88, 232, 272, 424, 464, 616, 656, 696, 808, 848, 888, 2112, 2552, 2992, 4224, 4664, 6336, 6776, 8008, 8448, 8888, 21112, 21312, 21512, 21712, 21912, 23032, 23232, 23432, 23632, 23832, 25152, 25352, 25552, 25752, 25952, 27072, 27272, 27472

Offset: 1

Jeff Burch

Paolo Xausa, Table of n, a(n) for n = 1..2000

Intersection of A002113 and A008590.

Cf. A029951, A045638, A045639, A043040, A043041, A045642, A045644, A083852.

palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]];Select[ 8Range[0,3500],palQ] (* Harvey P. Dale, Jun 06 2011 *)
Select[8*Range[0, 3500],PalindromeQ] (* Harvey P. Dale, Feb 17 2023 *)

Edited to include a(1) = 0 by Paolo Xausa, Jul 07 2025

A045644 Palindromic and divisible by 9.

Original entry on oeis.org

0, 9, 99, 171, 252, 333, 414, 585, 666, 747, 828, 909, 999, 1881, 2772, 3663, 4554, 5445, 6336, 7227, 8118, 9009, 9999, 10701, 11511, 12321, 13131, 14841, 15651, 16461, 17271, 18081, 18981, 19791, 20502, 21312, 22122, 23832, 24642, 25452, 26262

Offset: 1

Jeff Burch

Harvey P. Dale, Table of n, a(n) for n = 1..1001

Intersection of A002113 and A008591.

Cf. A029951, A045638, A045639, A043040, A043041, A045642, A045643, A083852.

Select[9*Range[0,3000],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 30 2020 *)

Edited to include a(1) = 0 by Paolo Xausa, Jul 07 2025

A029950 Odd palindromes.

Original entry on oeis.org

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

Offset: 1

Patrick De Geest

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

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

Subsequence of A002113.

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

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 *)

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

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

A045641 Palindromes that are divisible by 6.

Original entry on oeis.org

0, 6, 66, 222, 252, 282, 414, 444, 474, 606, 636, 666, 696, 828, 858, 888, 2112, 2442, 2772, 4224, 4554, 4884, 6006, 6336, 6666, 6996, 8118, 8448, 8778, 20202, 20502, 20802, 21012, 21312, 21612, 21912, 22122, 22422, 22722, 23232, 23532, 23832

Offset: 1

Jeff Burch

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Intersection of A002113 and A008588.

Cf. A029951, A045638, A045639, A043040, A045642, A045643, A045644, A083852.

Select[Range[0,30000,6], PalindromeQ] (* Paolo Xausa, Jul 06 2025 *)

A328333 Expansion of (1 + 4x - 6x^2) / ((1 - x) * (1 - 10*x^2)).

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Oct 12 2019

Number of even palindromes < 10^n.

Eric Weisstein's World of Mathematics, Palindromic Number
Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

Cf. A002113, A029951, A050250, A070199, A328332.

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]

Vec((1 + 4*x - 6*x^2) / ((1 - x) * (1 - 10*x^2)) + O(x^30)) \\ Michel Marcus, Oct 13 2019

cp's OEIS Frontend

A083852 Decimal palindromes that are multiples of 11.

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A043040 Numbers that are palindromic and divisible by 5.

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A045642 Palindromic and divisible by 7.

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A045638 Palindromic and divisible by 3.

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A045639 Palindromic and divisible by 4.

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A045643 Palindromic and divisible by 8.

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A045644 Palindromic and divisible by 9.

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A029950 Odd palindromes.

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A045641 Palindromes that are divisible by 6.

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A328333 Expansion of (1 + 4x - 6x^2) / ((1 - x) * (1 - 10*x^2)).