A287389 Both k and its reverse are one less than a square.

0, 3, 8, 80, 99, 323, 360, 575, 840, 4224, 5775, 9999, 32760, 36480, 36863, 42024, 84680, 349280, 808200, 829920, 848240, 998000, 999999, 3055503, 3272480, 3426200, 3640463, 3644280, 3682560, 5597955, 8462280, 8803088, 30481440, 32855823, 80622440, 99999999

Offset

1,2

Comments

Contains A028504. - Robert Israel, May 25 2017

Except for the first term, the first digit of each term is either 3, 4, 5, 8 or 9. - Chai Wah Wu, May 25 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 1..300 (terms n = 1..164 from Robert Israel)

Example

32760 is in the sequence because 32760 = 181^2-1 and its reverse 6723 = 82^2 - 1.

Maple

r:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
select(x-> issqr(r(x)+1), [n^2-1$n=1..10000])[]; # Alois P. Heinz, May 24 2017

Mathematica

Select[Range[0, 10^6], Function[n, Times @@ Boole@ Map[IntegerQ@ Sqrt@ # &, {n + 1, FromDigits@ Reverse@ IntegerDigits@ n + 1}] == 1]] (* Michael De Vlieger, May 24 2017 *)
Select[Range[0, 10^6], AllTrue[{Sqrt[#+1], Sqrt[IntegerReverse[#]+1]}, IntegerQ]&] (* The program generates the first 23 terms of the sequence. *) (* Harvey P. Dale, Dec 24 2025 *)

Prog

(PARI) isok(n) = issquare(n+1) && issquare(fromdigits(Vecrev(digits(n)))+1); \\ Michel Marcus, May 24 2017

Crossrefs

Cf. A124664: both k and its reverse are one more than a square.

Cf. A004086, A005563, A028504, A061457, A245361.

Sequence in context: A060752 A376941 A347641 * A233175 A347920 A367273

Adjacent sequences: A287386 A287387 A287388 * A287390 A287391 A287392

Keyword

nonn,base

Author

Bruno Berselli, May 24 2017

Status

approved