A029986 -id:A029986 - cp's OEIS frontend

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

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 *)

A263610 Palindromes in base 4 which are also squares.

Original entry on oeis.org

0, 1, 121, 10201, 12321, 1002001, 1032301, 1223221, 100020001, 102030201, 103101301, 120202021, 10000200001, 10033233001, 1000002000001, 1002003002001, 1003010103001, 1021320231201, 1211130311121, 1212110112121, 1213332333121, 100000020000001, 100033323330001, 100331000133001

Offset: 1

N. J. A. Sloane, Oct 22 2015

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, A029986, A262609, A029987.

A263609 Base-4 numbers whose square is a palindrome in base 4.

Original entry on oeis.org

0, 1, 11, 101, 111, 1001, 1013, 1103, 10001, 10101, 10121, 10331, 100001, 100133, 1000001, 1001001, 1001201, 1010301, 1100211, 1100323, 1101211, 10000001, 10001333, 10013201, 10031113, 100000001, 100010001, 100012001, 100103001, 100301113, 100332101, 101002101, 103231203, 110002011

Offset: 1

N. J. A. Sloane, Oct 22 2015

			From _Mattew Bondar_, Mar 12 2021: (Start)
111_4 = 21_10, 21^2 = 441, 441_10 = 12321_4 (palindrome).
1013_4 = 71_10, 71^2 = 5041, 5041_10 = 1032301_4 (palindrome). (End)

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

Cf. A002778, A029986, A263610, A029987.

FromDigits /@ IntegerDigits[Select[Range[0, 2^17], PalindromeQ@ IntegerDigits[#^2, 4] &], 4] (* Michael De Vlieger, Mar 13 2021 *)

def decimal_to_quaternary(n):
    if n == 0:
        return '0'
    b = ''
    while n > 0:
        b = str(n % 4) + b
        n = n // 4
    return b
x = 0
counter = 0
while True:
    y = decimal_to_quaternary(x ** 2)
    if y == y[::-1]:
        print(int(decimal_to_quaternary(x)))
        counter += 1
    x += 1  # Mattew Bondar, Mar 10 2021

cp's OEIS Frontend

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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A263610 Palindromes in base 4 which are also squares.

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A263609 Base-4 numbers whose square is a palindrome in base 4.

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