A029988 -id:A029988 - cp's OEIS frontend

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

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 *)

A030073 Numbers k such that k^2 is palindromic in base 15.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 12, 16, 19, 32, 39, 64, 76, 128, 144, 226, 241, 256, 271, 311, 452, 467, 478, 482, 576, 715, 904, 964, 1024, 1748, 1808, 1868, 2304, 2652, 2860, 3376, 3401, 3616, 3856, 4639, 6752, 6992, 7172, 8649, 10715, 13504, 13604

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), A030072 (b=14), this sequence (b=15), A029733 (b=16), A118651 (b=17).

p15Q[n_]:=Module[{id15=IntegerDigits[n^2,15]},id15==Reverse[id15]]; Select[ Range[0,14000],p15Q] (* Harvey P. Dale, Jun 03 2020 *)

A263612 Palindromes in base 5 which are also squares.

Original entry on oeis.org

0, 1, 4, 121, 10201, 12321, 114411, 1002001, 1234321, 100020001, 102030201, 121242121, 131141131, 10000200001, 10221412201, 12102420121, 131441144131, 1000002000001, 1002003002001, 1020304030201, 1143442443411, 1210024200121, 4133144413314, 4342230322434, 13431400413431, 100000020000001

Offset: 1

N. J. A. Sloane, Oct 23 2015

Terms displayed in base 5. - Harvey P. Dale, Jan 10 2023

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A002778, A003166, A029988, A262611, A029989.

FromDigits[IntegerDigits[#,5]]&/@Select[Range[0,100000]^2,IntegerDigits[ #,5] == Reverse[ IntegerDigits[ #,5]]&] (* Harvey P. Dale, Jan 10 2023 *)

A263611 Base 5 numbers whose square is a palindrome in base 5.

Original entry on oeis.org

0, 1, 2, 11, 101, 111, 231, 1001, 1111, 10001, 10101, 11011, 11204, 100001, 101101, 110011, 242204, 1000001, 1001001, 1010101, 1042214, 1100011, 2020303, 2043122, 2443304, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 111103411

Offset: 1

N. J. A. Sloane, Oct 23 2015

A029988 expressed in base 5.

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A007091, A002778, A029988, A263612, A029989.

With[{b = 5}, FromDigits@ IntegerDigits[#, b] & /@ Select[Range[b^9], PalindromeQ[IntegerDigits[#^2, b]] &]] (* Michael De Vlieger, Aug 15 2022 *)

a(n) = A007091(A029988(n)).

Name corrected by Charles R Greathouse IV, Aug 15 2022

cp's OEIS Frontend

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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A030073 Numbers k such that k^2 is palindromic in base 15.

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A263612 Palindromes in base 5 which are also squares.

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A263611 Base 5 numbers whose square is a palindrome in base 5.

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