A029733 -id:A029733 - cp's OEIS frontend

A029986 Numbers k such that k^2 is palindromic in base 4.

0, 1, 5, 17, 21, 65, 71, 83, 257, 273, 281, 317, 1025, 1055, 4097, 4161, 4193, 4401, 5157, 5179, 5221, 16385, 16511, 16865, 17239, 65537, 65793, 65921, 66753, 68695, 69521, 69777, 80739, 82053, 82171, 82309, 82885, 83301, 262145

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A007090, A014192.

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), this sequence (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

Select[Range[0,300000],IntegerDigits[#^2,4]==Reverse[ IntegerDigits[ #^2,4]]&] (* Harvey P. Dale, Dec 01 2015 *)

isok(k) = my(d=digits(k^2,4)); d == Vecrev(d); \\ Michel Marcus, Jul 04 2021

A029990 Numbers k such that k^2 is palindromic in base 6.

Original entry on oeis.org

0, 1, 2, 7, 37, 43, 76, 91, 217, 259, 1064, 1297, 1333, 1519, 1555, 2704, 3367, 7777, 8029, 9079, 19747, 46657, 46873, 47989, 48205, 54439, 54655, 54695, 83979, 118027, 241304, 279937, 281449, 287749, 326599, 707707, 1679617

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..92
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A007092.

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), this sequence (b=6), A029992 (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

palindromicQ[n_, b_:10] := TrueQ[IntegerDigits[n, b] == Reverse[IntegerDigits[n, b]]]; Select[Range[1000], palindromicQ[#^2, 6] &] (* Alonso del Arte, Mar 05 2017 *)

ispal(n,base)=my(d=digits(n,base)); d==Vecrev(d)
is(n)==ispal(n^2,6) \\ Charles R Greathouse IV, Mar 09 2017

A029992 Numbers k such that k^2 is palindromic in base 7.

Original entry on oeis.org

0, 1, 2, 4, 8, 10, 11, 20, 32, 40, 50, 57, 64, 80, 160, 200, 344, 400, 500, 550, 557, 730, 1000, 1376, 1432, 1892, 2402, 2451, 2500, 2752, 2801, 3440, 3784, 3902, 5101, 5266, 6880, 8296, 9460, 9608, 9804, 16808, 17200, 19216, 19608, 22693

Offset: 1

Patrick De Geest

			8^2 = 64, which is 121 in base 7, and since that's palindromic, 8 is in the sequence.
9^2 = 81, which is 144 in base 7, but since that's not palindromic, 9 is not in the sequence.

Marius A. Burtea, Table of n, a(n) for n = 1..237
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A002440 (squares written in base 7), A007093.

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), this sequence (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

[k:k in [0..23000]| Seqint(Intseq(k^2,7)) eq Seqint(Reverse(Intseq(k^2,7)))]; // Marius A. Burtea, Jan 22 2020

Select[Range[0, 16806], IntegerDigits[#^2, 7] == Reverse[IntegerDigits[#^2, 7]] &] (* Alonso del Arte, Jan 21 2020 *)

(0 to 16806).filter(n => Integer.toString(n * n, 7) == Integer.toString(n * n, 7).reverse) // Alonso del Arte, Jan 21 2020

A029805 Numbers k such that k^2 is palindromic in base 8.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 11, 27, 65, 73, 79, 81, 83, 195, 219, 237, 366, 513, 543, 585, 697, 1094, 1539, 1755, 1875, 2910, 4097, 4161, 4225, 4477, 4617, 4681, 4727, 4891, 5267, 8698, 8730, 11841, 12291, 12483, 12675, 13065, 13851, 14673, 15021

Offset: 1

Patrick De Geest

The only powers of 2 in this sequence are 1 and 2. - Alonso del Arte, Feb 25 2017

			3 is in the sequence because 3^2 = 9 = 11 in base 8, which is a palindrome.
4 is not in the sequence because 4^2 = 16 = 20 in base 8, which is not a palindrome.

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A000290, A002441, A007094.

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), this sequence (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[Range[0, 16000], palQ[#^2, 8] &] (* Harvey P. Dale, May 19 2012 *)

from itertools import count, islice
def A029805_gen(): # generator of terms
    return filter(lambda k: (s:=oct(k**2)[2:])[:(t:=(len(s)+1)//2)]==s[:-t-1:-1],count(0))
A029805_list = list(islice(A029805_gen(),20)) # Chai Wah Wu, Jun 23 2022

A029994 Numbers k such that k^2 is palindromic in base 9.

Original entry on oeis.org

0, 1, 2, 10, 20, 82, 91, 100, 164, 730, 820, 1460, 6562, 6643, 6724, 7300, 7381, 7462, 13124, 13642, 13660, 14281, 54050, 59050, 59860, 65620, 66430, 118100, 123010, 126286, 161410, 161896, 487750, 531442, 532171

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A007095.

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), A029805 (b=8), this sequence (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

pb9Q[n_]:=Module[{idn=IntegerDigits[n^2,9]},idn==Reverse[idn]]; Select[ Range[0,600000],pb9Q] (* Harvey P. Dale, Sep 29 2013 *)

A029996 Numbers k such that k^2 is palindromic in base 11.

Original entry on oeis.org

0, 1, 2, 3, 6, 12, 24, 26, 72, 84, 122, 133, 144, 244, 255, 279, 382, 732, 1332, 1464, 1596, 2414, 2664, 2796, 3062, 4476, 7992, 14642, 14763, 14884, 15984, 16105, 16226, 17326, 29284, 29405, 30626, 33675, 34701, 63546, 87246, 87852, 88578

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), this sequence (b=11), A029737 (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

A118651 Numbers k such that k^2 is a palindrome when written in base 17.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 12, 18, 28, 36, 84, 108, 290, 307, 324, 341, 580, 597, 614, 1080, 1614, 1740, 1842, 2616, 3378, 3480, 3720, 4344, 4824, 4914, 5220, 5526, 6408, 9828, 10134, 10440, 14472, 17944, 19336, 24360, 27624, 29484, 31320, 33144, 33960

Offset: 1

Neven Juric (neven.juric(AT)apis-it.hr), May 12 2006

			E.g. 4^2 = 16_10 = G_16, 6^2 = 36_10 = 22_17, etc.

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A029984 for base 3, A029986 for base 4, A029988 for base 5, A029990 for base 6, A029992 for base 7, A029805 for base 8, A029994 for base 9, A002778 for base 10, A029996 for base 11, A029733 for base 16

Cf. also A016106, A028818, A059744, A059745.

A029737 Numbers whose square is palindromic in base 12.

Original entry on oeis.org

0, 1, 2, 3, 13, 26, 145, 157, 169, 179, 181, 290, 292, 302, 611, 1729, 1745, 1783, 1885, 2041, 3458, 3614, 3796, 20737, 20881, 21025, 21169, 22477, 22621, 22765, 24073, 24217, 24361, 24599, 25523, 25579, 28613, 41474, 41618, 41908, 43214

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), this sequence (b=12), A029998 (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

pal12Q[n_]:=Module[{idn12=IntegerDigits[n^2,12]},idn12==Reverse[idn12]]
Select[Range[0,50000],pal12Q]  (* Harvey P. Dale, Feb 06 2011 *)

A029998 Numbers k such that k^2 is palindromic in base 13.

Original entry on oeis.org

0, 1, 2, 3, 14, 28, 170, 183, 196, 209, 308, 340, 353, 366, 2198, 2380, 2562, 2898, 4026, 4242, 4396, 4578, 7078, 7662, 28562, 28731, 28900, 29069, 30772, 30941, 31110, 32813, 32982, 33151, 37374, 51510, 52360, 54942, 55449, 57124, 57293

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), this sequence (b=13), A030072 (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

A030072 Numbers k such that k^2 is palindromic in base 14.

Original entry on oeis.org

0, 1, 2, 3, 15, 24, 30, 47, 165, 197, 211, 225, 239, 394, 408, 422, 2190, 2445, 2745, 2955, 3165, 5490, 5700, 8565, 38417, 38613, 38809, 39005, 41175, 41371, 41567, 41763, 43737, 43933, 44129, 48159, 55962, 76834, 77030, 77226, 79592, 79788

Offset: 1

Patrick De Geest

Seiichi Manyama, Table of n, a(n) for n = 1..100
Patrick De Geest, Palindromic Squares in bases 2 to 17

Numbers k such that k^2 is palindromic in base b: A003166 (b=2), A029984 (b=3), A029986 (b=4), A029988 (b=5), A029990 (b=6), A029992 (b=7), A029805 (b=8), A029994 (b=9), A002778 (b=10), A029996 (b=11), A029737 (b=12), A029998 (b=13), this sequence (b=14), A030073 (b=15), A029733 (b=16), A118651 (b=17).

pal14Q[n_]:=Module[{idn14=IntegerDigits[n^2,14]},idn14==Reverse[idn14]]; Select[Range[0,80000],pal14Q] (* Harvey P. Dale, Mar 09 2012 *)

cp's OEIS Frontend

A029986 Numbers k such that k^2 is palindromic in base 4.

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PARI

A029990 Numbers k such that k^2 is palindromic in base 6.

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A029992 Numbers k such that k^2 is palindromic in base 7.

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A029805 Numbers k such that k^2 is palindromic in base 8.

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A029994 Numbers k such that k^2 is palindromic in base 9.

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A029996 Numbers k such that k^2 is palindromic in base 11.

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A118651 Numbers k such that k^2 is a palindrome when written in base 17.

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A029737 Numbers whose square is palindromic in base 12.

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A029998 Numbers k such that k^2 is palindromic in base 13.

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A030072 Numbers k such that k^2 is palindromic in base 14.

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