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

1,3

Links

Marius A. Burtea, Table of n, a(n) for n = 1..237

Patrick De Geest, Palindromic Squares

Example

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.

Mathematica

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

Prog

(Scala) (0 to 16806).filter(n => Integer.toString(n * n, 7) == Integer.toString(n * n, 7).reverse) // Alonso del Arte, Jan 21 2020
(Magma) [k:k in [0..23000]| Seqint(Intseq(k^2, 7)) eq Seqint(Reverse(Intseq(k^2, 7)))]; // Marius A. Burtea, Jan 22 2020

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).

Sequence in context: A070305 A174567 A178330 * A346139 A206928 A133012

Adjacent sequences: A029989 A029990 A029991 * A029993 A029994 A029995

Keyword

nonn,base

Author

Patrick De Geest

Status

approved