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A057135 Palindromes whose square is a palindrome; also palindromes whose sum of squares of digits is less than 10. 7
0, 1, 2, 3, 11, 22, 101, 111, 121, 202, 212, 1001, 1111, 2002, 10001, 10101, 10201, 11011, 11111, 11211, 20002, 20102, 100001, 101101, 110011, 111111, 200002, 1000001, 1001001, 1002001, 1010101, 1011101, 1012101, 1100011, 1101011, 1102011, 1110111, 1111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000 (n=1..412 from R. J. Mathar)

P. De Geest, Subsets of Palindromic Squares

FORMULA

a(n) = sqrt(A057136(n))

EXAMPLE

121 is OK since 121^2=14641 is also a palindrome.

MAPLE

dmax:= 7: # to get all terms with up to dmax digits

Res:= 0, 1, 2, 3, 11, 22:

Po:= [[0], [1], [2], [3]]: Pe:= [[0, 0], [1, 1], [2, 2]]:

for d from 1 to dmax do

  if d::odd then

    Po:= select(t -> add(s^2, s=t) < 10, [seq(seq([i, op(t), i], t=Po), i=0..2)]);

    Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1), i=1..nops(p)) fi end proc, Po))

  else

    Pe:= select(t -> add(s^2, s=t) < 10, [seq(seq([i, op(t), i], t=Pe), i=0..2)]);

    Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1), i=1..nops(p)) fi end proc, Pe))

  fi;

od:

Res; # Robert Israel, Jun 21 2017

MATHEMATICA

PalQ[n_] := FromDigits[Reverse[IntegerDigits[n]]] == n; t = {}; Do[

If[PalQ[n] && PalQ[n^2], AppendTo[t, n]], {n, 0, 1200000}]; t (* Jayanta Basu, May 10 2013 *)

PROG

(PARI) is(n) = digits(n)==Vecrev(digits(n)) && digits(n^2)==Vecrev(digits(n^2)) \\ Felix Fröhlich, Jun 21 2017

CROSSREFS

Cf. A000290, A002113, A002779, A057136, A128921.

Sequence in context: A229549 A229804 A241096 * A229805 A104075 A236168

Adjacent sequences:  A057132 A057133 A057134 * A057136 A057137 A057138

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Aug 12 2000

EXTENSIONS

1001001 inserted by R. J. Mathar, Nov 04 2012

STATUS

approved

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Last modified July 21 02:56 EDT 2017. Contains 289629 sequences.