A043040 -id:A043040 - cp's OEIS frontend

A045640 Duplicate of A043040.

5, 55, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 5005, 5115, 5225

Offset: 1

dead

A029951 Even palindromes.

0, 2, 4, 6, 8, 22, 44, 66, 88, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 606, 616, 626, 636, 646, 656, 666, 676, 686, 696, 808, 818, 828, 838, 848, 858, 868, 878, 888, 898, 2002, 2112, 2222

Offset: 1

Patrick De Geest

John Cerkan, Table of n, a(n) for n = 1..10000
Patrick De Geest, World!Of Numbers

Cf. A002113 (superset), A062287 (subset), A367807 (halved).

Cf. A045638, A045639, A043040, A045641, A045642, A045643, A045644, A083852.

palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Select[Range[2, 10^4, 2], palindromicQ[#] &] (* Alonso del Arte, Feb 23 2012 *)
Select[Range[0, 2222, 2], PalindromeQ] (* Michael De Vlieger, May 12 2017, Version 10.3 *)

A083852 Decimal palindromes that are multiples of 11.

Original entry on oeis.org

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

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

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 *)

A337184 Numbers divisible by their first digit and their last digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 101, 102, 104, 105, 111, 112, 115, 121, 122, 123, 124, 125, 126, 128, 131, 132, 135, 141, 142, 144, 145, 147, 151, 152, 153, 155, 156, 161, 162, 164, 165, 168, 171, 172, 175, 181, 182

Offset: 1

Bernard Schott, Jan 29 2021

The first 23 terms are the same first 23 terms of A034838 then a(24) = 101 while A034838(24) = 111.
Terms of A034709 beginning with 1 and terms of A034837 ending with 1 are terms.
All positive repdigits (A010785) are terms.
There are infinitely many terms m for any of the 53 pairs (first digit, last digit) of m described below: when m begins with {1, 3, 7, 9} then m ends with any digit from 1 to 9; when m begins with {2, 4, 6, 8}, then m must also end with {2, 4, 6, 8}; to finish, when m begins with 5, m must only end with 5. - Metin Sariyar, Jan 29 2021

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Intersection of A034709 and A034837.
Subsequences: A010785\{0}, A034838, A043037, A043040, A208259, A066622.
Cf. A139138.

Select[Range[175], Mod[#, 10] > 0 && And @@ Divisible[#, IntegerDigits[#][[{1, -1}]]] &] (* Amiram Eldar, Jan 29 2021 *)

is(n) = n%10>0 && n%(n%10)==0 && n % (n\10^logint(n,10)) == 0 \\ David A. Corneth, Jan 29 2021

def ok(n): s = str(n); return s[-1] != '0' and n%int(s[0])+n%int(s[-1]) == 0
print([m for m in range(180) if ok(m)]) # Michael S. Branicky, Jan 29 2021

(10n-9)/9 <= a(n) < 45n. (I believe the liminf of a(n)/n is 3.18... and the limsup is 6.18....) - Charles R Greathouse IV, Nov 26 2024

Conjecture: 3n < a(n) < 7n for n > 75. - Charles R Greathouse IV, Dec 02 2024

cp's OEIS Frontend

A045640 Duplicate of A043040.

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A029951 Even palindromes.

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A083852 Decimal palindromes that are multiples of 11.

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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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A045641 Palindromes that are divisible by 6.

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Mathematica

A337184 Numbers divisible by their first digit and their last digit.

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