A278328 Numbers n such that abs(n - rev(n)) is a square, where rev(n) is the decimal reverse of n (A004086).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 21, 22, 23, 26, 32, 33, 34, 37, 40, 43, 44, 45, 48, 51, 54, 55, 56, 59, 62, 65, 66, 67, 73, 76, 77, 78, 84, 87, 88, 89, 90, 95, 98, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262

Offset: 1

Author

Jonathan Frech, Nov 18 2016

Keywords

• nonn
• base

Comments

All palindromes are in this sequence, hence it is infinite.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

A002113 is a subsequence.

Cf. A000290, A004086, A016766, A056965.

Programs

Maple

a:= proc(n) option remember; local k; for k from 1+
      `if`(n=1, -1, a(n-1)) while not issqr(abs(k-(s->
       parse(cat(s[-i]$i=1..length(s))))(""||k))) do od: k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 18 2016

Mathematica

Select[Range@ 262, IntegerQ@ Sqrt@ Abs[# - FromDigits@ Reverse@ IntegerDigits@ #] &] (* Michael De Vlieger, Nov 18 2016 *)

PARI

is(n) = issquare(abs(n - eval(concat(Vecrev(Str(n)))))) \\ Felix Fröhlich, Nov 18 2016

PARI

is(n, {b=10}) = issquare(abs(n - subst(Polrev(digits(n, b),'x),'x,b))); \\ Gheorghe Coserea, Nov 27 2016

Python

import math
n = 0
while True:
    if math.sqrt(abs(n-int(str(n)[::-1])))%1 == 0:
        print(n)
    n += 1 # Jonathan Frech, Nov 18 2016