A029983 -id:A029983 - 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

A229687 Odd squares whose binary reversal is also a square.

Original entry on oeis.org

1, 9, 20457529, 143784081, 331130809, 4365905625, 5216450625, 20074072489, 1193532215121, 10036851273801, 36014509461681, 38767247532225, 41413201925481, 155991531977649, 320642706437001, 2543173099393689, 2696589987547401, 4665141483989281, 87463589042698969

Offset: 1

Alex Ratushnyak, Dec 19 2013

The sequence of binary reversals that are squares is a permutation of a(n), it begins: 1, 9, 20457529, 143784081, 331130809, 5216450625, 4365905625, 20074072489, 1193532215121, 10036851273801, 38767247532225, 36014509461681, ...

A029983 is a subsequence (after zero). - Antti Karttunen, Dec 20 2013

Cf. A000290, A029983, A074832, A229766.

#include 
#include 
int main() {
  unsigned long long n, t, r, sr;
  for (n=1; n<(1ULL<<32); n+=2) {
     t = n*n;
     r = 0;
     while (t)  r = r*2+(t&1),  t >>= 1;
     sr = sqrt(r);
     if (sr*sr==r)  printf("%llu, ", n*n);
  }
  return 0;
}

(define (A229687 n) (A000290 (A229766 n))) ;; Antti Karttunen, Dec 20 2013

a(n) = A229766(n)^2.

A272711 Square numbers whose binary reversal is also square.

Original entry on oeis.org

1, 4, 9, 16, 36, 64, 144, 256, 576, 1024, 2304, 4096, 9216, 16384, 36864, 65536, 147456, 262144, 589824, 1048576, 2359296, 4194304, 9437184, 16777216, 20457529, 37748736, 67108864, 81830116, 143784081, 150994944, 268435456, 327320464, 331130809, 575136324, 603979776

Offset: 1

Benjamin Przybocki, May 04 2016

The first term in this sequence whose binary reversal is not 1 or 9 is 20457529 (which is a binary palindrome).
The previous comment means that the sequence does not just contain the squares of numbers in A029744. - R. J. Mathar, May 06 2016
If k is a term, then so is 4*k. - Robert Israel, Jun 06 2023

Robert Israel, Table of n, a(n) for n = 1..176

Cf. A000290, A030101, A029983, A229687.

Cf. A061457 (analogous in base 10).

rev:= proc(n) local L,i;
  L:= convert(n,base,2);
  add(L[-i]*2^(i-1),i=1..nops(L))
end proc:
select(n -> issqr(rev(n)), [seq(i^2,i=1..100000)]); # Robert Israel, Jun 06 2023

Select[Range[10^5]^2, IntegerQ@ Sqrt@ FromDigits[ Reverse@ IntegerDigits[#, 2], 2] &] (* Giovanni Resta, May 05 2016 *)

lista(nn) = {for (n=1, nn, if (issquare(subst(Polrev(binary(n^2)), x, 2)), print1(n^2, ", ")););} \\ Michel Marcus, May 05 2016

A225300 Terms in A025475 that are palindromes in base 2.

Original entry on oeis.org

1, 9, 27, 20457529, 87463589042698969

Offset: 1

Alex Ratushnyak, May 04 2013

			9 = 1001_2.
27 = 11011_2.
20457529 = 1001110000010100000111001_2.

Intersection of A006995 and A025475.

Cf. A029983.

Definition clarified by Chai Wah Wu, Mar 18 2018

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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A229687 Odd squares whose binary reversal is also a square.

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A272711 Square numbers whose binary reversal is also square.

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Maple

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A225300 Terms in A025475 that are palindromes in base 2.

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