A029985 -id:A029985 - cp's OEIS frontend

A030074 Squares which are palindromes in base 14.

0, 1, 4, 9, 225, 576, 900, 2209, 27225, 38809, 44521, 50625, 57121, 155236, 166464, 178084, 4796100, 5978025, 7535025, 8732025, 10017225, 30140100, 32490000, 73359225, 1475865889, 1490963769, 1506138481, 1521390025

Offset: 1

Patrick De Geest

Vincenzo Librandi, Table of n, a(n) for n = 1..57
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A002779, A029734, A029738, A029806, A029983, A029985, A029987, A029989, A029991, A029993, A029995, A029997, A029999, A030075.

pb14Q[n_]:=Module[{idn14=IntegerDigits[n, 14]}, idn14==Reverse[idn14]]; Select[Range[0, 20000]^2, pb14Q] (* Vincenzo Librandi, Jul 24 2014 *)

A030075 Squares which are palindromes in base 15.

Original entry on oeis.org

0, 1, 4, 9, 16, 64, 144, 256, 361, 1024, 1521, 4096, 5776, 16384, 20736, 51076, 58081, 65536, 73441, 96721, 204304, 218089, 228484, 232324, 331776, 511225, 817216, 929296, 1048576, 3055504, 3268864, 3489424, 5308416, 7033104

Offset: 1

Patrick De Geest

			8^2 = 64, which in base 15 is 44, and that's palindromic, so 64 is in the sequence.
9^2 = 81, which in base 15 is 56. Since that's not palindromic, 81 is not in the sequence.

Vincenzo Librandi, Table of n, a(n) for n = 1..106
Patrick De Geest, Palindromic Squares in bases 2 to 17

Cf. A002779, A029734, A029738, A029806, A029983, A029985, A029987, A029989, A029991, A029993, A029995, A029997, A029999, A030074.

N:= 10^10: # to get all entries <= N
count:= 0:
for x from 0 to floor(sqrt(N)) do
    y:= x^2;
    L:= convert(y,base,15);
  if ListTools[Reverse](L) = L then
     count:= count+1;
     A[count]:= y;
   fi
od:
seq(A[i],i=1..count); # Robert Israel, Jul 24 2014

palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[Range[0, 2700]^2, palQ[#, 15] &]  (* Harvey P. Dale, Apr 23 2011 *)

isok(n) = my(d=digits(n,15)); issquare(n) && (d == Vecrev(d)); \\ Michel Marcus, Oct 21 2016

A263607 Base 3 numbers whose square is a palindrome in base 3.

Original entry on oeis.org

0, 1, 2, 11, 101, 102, 202, 211, 1001, 1021, 2002, 10001, 10022, 11012, 12201, 20002, 100001, 100201, 200002, 201102, 1000001, 1000222, 1002201, 1011221, 1101211, 1211201, 1212022, 2000002, 10000001, 10002001, 10200102, 10201121, 11011211, 12212101, 20000002, 20011002, 100000001, 100002222, 100022001

Offset: 1

N. J. A. Sloane, Oct 22 2015

Chai Wah Wu, Table of n, a(n) for n = 1..288
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A002778, A029984, A263608, A029985.

A263608 Palindromes which are base-3 representations of squares.

Original entry on oeis.org

0, 1, 11, 121, 10201, 11111, 112211, 122221, 1002001, 1120211, 11022011, 100020001, 101212101, 122111221, 1012112101, 1100220011, 10000200001, 10111011101, 110002200011, 111221122111, 1000002000001, 1001221221001, 1012200022101, 1101202021011, 1221221221221, 10101111110101

Offset: 1

N. J. A. Sloane, Oct 22 2015

Robert Israel, Table of n, a(n) for n = 1..143
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A002778, A003166, A029984, A262607, A029985.

Intersection of A001738 and A118594.

rev3:= proc(n) local L,i; L:= convert(n,base,3); add(L[-i]*3^(i-1),i=1..nops(L)) end proc:
c3:= proc(n) local L,i; L:= convert(n,base,3); add(L[i]*10^(i-1),i=1..nops(L)) end proc:
R:= 0,1: count:= 2:
for d from 2 while count < 100 do
    if d::odd then
      V:= select(issqr, [seq(seq(a*3^((d+1)/2) + b*3^((d-1)/2)+rev3(a),b=0..2),a=3^((d-3)/2) .. 3^((d-1)/2)-1)])
    else
      V:= select(issqr, [seq(a*3^(d/2) + rev3(a), a=3^(d/2-1) .. 3^(d/2)-1)]);
    fi;
    count:= count+nops(V);
    R:= R, op(map(c3,V));
od:
R; # Robert Israel, May 19 2024

Name edited by Robert Israel, May 19 2024

cp's OEIS Frontend

A030074 Squares which are palindromes in base 14.

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A030075 Squares which are palindromes in base 15.

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A263607 Base 3 numbers whose square is a palindrome in base 3.

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A263608 Palindromes which are base-3 representations of squares.

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