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A278328 Numbers n such that abs(n - rev(n)) is a square, where rev(n) is the decimal reverse of n (A004086). 2

%I #54 May 04 2017 14:32:36

%S 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,

%T 48,51,54,55,56,59,62,65,66,67,73,76,77,78,84,87,88,89,90,95,98,99,

%U 101,111,121,131,141,151,161,171,181,191,202,212,222,232,242,252,262

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

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

%H Alois P. Heinz, <a href="/A278328/b278328.txt">Table of n, a(n) for n = 1..20000</a>

%p a:= proc(n) option remember; local k; for k from 1+

%p `if`(n=1, -1, a(n-1)) while not issqr(abs(k-(s->

%p parse(cat(s[-i]$i=1..length(s))))(""||k))) do od: k

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Nov 18 2016

%t Select[Range@ 262, IntegerQ@ Sqrt@ Abs[# - FromDigits@ Reverse@ IntegerDigits@ #] &] (* _Michael De Vlieger_, Nov 18 2016 *)

%o (Python 2.7.7)

%o import math

%o n = 0

%o while True:

%o if math.sqrt(abs(n-int(str(n)[::-1])))%1 == 0:

%o print n

%o n += 1 # _Jonathan Frech_, Nov 18 2016

%o (PARI) is(n) = issquare(abs(n - eval(concat(Vecrev(Str(n)))))) \\ _Felix Fröhlich_, Nov 18 2016

%o (PARI) is(n, {b=10}) = issquare(abs(n - subst(Polrev(digits(n, b),'x),'x,b))); \\ _Gheorghe Coserea_, Nov 27 2016

%Y A002113 is a subsequence.

%Y Cf. A000290, A004086, A016766, A056965.

%K nonn,base

%O 1,3

%A _Jonathan Frech_, Nov 18 2016

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)