A029989 -id:A029989 - 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

A081502 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 3x+y.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 21, 22, 23, 24, 25, 26, 27, 28, 29

Offset: 0

N. J. A. Sloane, Apr 22 2003

Eswaran observes that n is divisible by 7 iff repeated application of a ends at the number 7.

a(n) is divisible by 7 iff n is divisible by 7: e.g., a(7) = a(14) = a(21) = 7, a(28) = a(35) = a(42) = 14 etc. - Zak Seidov, Mar 19 2014

R. Eswaran, Test of divisibility of the number 7, Abstracts Amer. Math. Soc., 23 (No. 2, 2002), #974-00-5, p. 275.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Different from A028898 for n>=100 (e.g. a(111) = 34, A029989(111) = 13).

Cf. A081503, A081594, A081595, A081596, A081597, A081598, A081599, A081600.

A081502 := proc(n)
    local x,y ;
    y := modp(n,10) ;
    x := iquo(n,10) ;
    3*x+y ;
end proc:
seq(A081502(n),n=0..120) ; # R. J. Mathar, Oct 03 2014

Table[n - 7 * Floor[n / 10], {n, 0, 100}] (* Joshua Oliver, Dec 04 2019 *)

a(n) = 3*(n\10) + (n % 10); \\ Michel Marcus, Mar 19 2014

a(n) = [3,1]*divrem(n,10); \\ Kevin Ryde, Dec 04 2019

G.f.: -x*(6*x^9-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x-1) / (x^11-x^10-x+1). - Colin Barker, Mar 19 2014

a(n) = n-7*floor(n/10). - Wesley Ivan Hurt, May 12 2016

A263612 Palindromes in base 5 which are also squares.

Original entry on oeis.org

0, 1, 4, 121, 10201, 12321, 114411, 1002001, 1234321, 100020001, 102030201, 121242121, 131141131, 10000200001, 10221412201, 12102420121, 131441144131, 1000002000001, 1002003002001, 1020304030201, 1143442443411, 1210024200121, 4133144413314, 4342230322434, 13431400413431, 100000020000001

Offset: 1

N. J. A. Sloane, Oct 23 2015

Terms displayed in base 5. - Harvey P. Dale, Jan 10 2023

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, A029988, A262611, A029989.

FromDigits[IntegerDigits[#,5]]&/@Select[Range[0,100000]^2,IntegerDigits[ #,5] == Reverse[ IntegerDigits[ #,5]]&] (* Harvey P. Dale, Jan 10 2023 *)

A263611 Base 5 numbers whose square is a palindrome in base 5.

Original entry on oeis.org

0, 1, 2, 11, 101, 111, 231, 1001, 1111, 10001, 10101, 11011, 11204, 100001, 101101, 110011, 242204, 1000001, 1001001, 1010101, 1042214, 1100011, 2020303, 2043122, 2443304, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 111103411

Offset: 1

N. J. A. Sloane, Oct 23 2015

A029988 expressed in base 5.

G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A007091, A002778, A029988, A263612, A029989.

With[{b = 5}, FromDigits@ IntegerDigits[#, b] & /@ Select[Range[b^9], PalindromeQ[IntegerDigits[#^2, b]] &]] (* Michael De Vlieger, Aug 15 2022 *)

a(n) = A007091(A029988(n)).

Name corrected by Charles R Greathouse IV, Aug 15 2022

cp's OEIS Frontend

A030074 Squares which are palindromes in base 14.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A030075 Squares which are palindromes in base 15.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A081502 Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 3x+y.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI

Formula

A263612 Palindromes in base 5 which are also squares.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A263611 Base 5 numbers whose square is a palindrome in base 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions