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

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

Author

Patrick De Geest

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

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).

Programs

Magma

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

Mathematica

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

Scala

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