A263608 -id:A263608

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A029984

Numbers k such that k^2 is palindromic in base 3.

+10
17

0, 1, 2, 4, 10, 11, 20, 22, 28, 34, 56, 82, 89, 113, 154, 164, 244, 262, 488, 524, 730, 755, 802, 862, 1021, 1342, 1358, 1460, 2188, 2242, 2684, 2716, 3046, 4276, 4376, 4484, 6562, 6641, 6778, 8030, 8215, 8350, 8887, 12482, 13124, 14810, 19684

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..400 (first 100 terms from Harvey P. Dale)

P. De Geest, Palindromic Squares

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

MATHEMATICA

pal3Q[n_]:=Module[{idn3=IntegerDigits[n^2, 3]}, idn3==Reverse[idn3]]; Select[Range[0, 20000], pal3Q] (* Harvey P. Dale, May 22 2012 *)

CROSSREFS

Cf. A002778, A003166, A007089, A029985, A263607, A263608.

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

STATUS

approved

A029985

Squares which are palindromes in base 3.

+10
15

0, 1, 4, 16, 100, 121, 400, 484, 784, 1156, 3136, 6724, 7921, 12769, 23716, 26896, 59536, 68644, 238144, 274576, 532900, 570025, 643204, 743044, 1042441, 1800964, 1844164, 2131600, 4787344, 5026564, 7203856, 7376656, 9278116

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..521

Patrick De Geest, Palindromic Squares

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

MATHEMATICA

b3pQ[n_]:=Module[{idn3=IntegerDigits[n, 3]}, idn3==Reverse[idn3]]; Select[ Range[0, 3200]^2, b3pQ] (* Harvey P. Dale, Aug 07 2011 *)

CROSSREFS

Cf. A029984, A263607, A263608; also A002778, A003166.

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

STATUS

approved

A263607

Base 3 numbers whose square is a palindrome in base 3.

+10
4

0, 1, 2, 11, 101, 102, 202, 211, 1001, 1021, 2002, 10001, 10022, 11012, 12201, 20002, 100001, 100201, 200002, 201102, 1000001, 1000222, 1002201, 1011221, 1101211, 1211201, 1212022, 2000002, 10000001, 10002001, 10200102, 10201121, 11011211, 12212101, 20000002, 20011002, 100000001, 100002222, 100022001

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..288

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

CROSSREFS

Cf. A002778, A029984, A263608, A029985.

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Oct 22 2015

STATUS

approved

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