A028504 -id:A028504 - cp's OEIS frontend

A070254 Perfect squares one more than a palindrome.

1, 4, 9, 100, 324, 576, 4225, 5776, 10000, 36864, 42025, 1000000, 3055504, 3640464, 5597956, 8803089, 32855824, 100000000, 360696064, 422919225, 10000000000, 30485858404, 30536863504, 32154945124, 59080108096, 86310801369, 304816618404, 1000000000000, 3490500050944

Offset: 1

Amarnath Murthy, May 06 2002

All even powers of 10 are members of both A070254 and A027720.

Giovanni Resta, Table of n, a(n) for n = 1..53

Cf. A028504, A027719, A027720, A070253.

Do[ If[a = IntegerDigits[n^2 - 1]; a == Reverse[a], Print[n^2]], {n, 1, 10^6}]
Select[Range[300000]^2,PalindromeQ[#-1]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 06 2018 *)

a(n) = A070253(n)^2 = A028504(n) + 1. - Giovanni Resta, Aug 29 2018

Edited by Jason Earls and Robert G. Wilson v, May 08 2002

Offset changed by and more terms from Giovanni Resta, Aug 28 2018

A028503 Numbers k such that k*(k+2) is a palindrome.

Original entry on oeis.org

0, 1, 2, 9, 17, 23, 64, 75, 99, 191, 204, 999, 1747, 1907, 2365, 2966, 5731, 9999, 18991, 20564, 99999, 174601, 174747, 179317, 243063, 293786, 552101, 999999, 1868287, 2967032, 9200156, 9999999, 22765895, 31552659, 93809716, 99999999, 185812387, 999999999

Offset: 1

Patrick De Geest

Giovanni Resta, Table of n, a(n) for n = 1..53
P. De Geest, Palindromic quasipronic numbers of the form n(n+2)

Cf. A005563, A028504, A070253.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; Select[Range[0, 10^5], palQ[# (# + 2)] &] (* Giovanni Resta, Aug 29 2018 *)

a(n) = A070253(n) - 1. a(n) * (a(n) + 2) = A028504(n). - Giovanni Resta, Aug 29 2018

More terms from Giovanni Resta, Aug 28 2018

A287389 Both k and its reverse are one less than a square.

Original entry on oeis.org

0, 3, 8, 80, 99, 323, 360, 575, 840, 4224, 5775, 9999, 32760, 36480, 36863, 42024, 84680, 349280, 808200, 829920, 848240, 998000, 999999, 3055503, 3272480, 3426200, 3640463, 3644280, 3682560, 5597955, 8462280, 8803088, 30481440, 32855823, 80622440, 99999999

Offset: 1

Bruno Berselli, May 24 2017

Contains A028504. - Robert Israel, May 25 2017

Except for the first term, the first digit of each term is either 3, 4, 5, 8 or 9. - Chai Wah Wu, May 25 2017

			32760 is in the sequence because 32760 = 181^2-1 and its reverse 6723 = 82^2 - 1.

Chai Wah Wu, Table of n, a(n) for n = 1..300 (terms n = 1..164 from Robert Israel)

Cf. A124664: both k and its reverse are one more than a square.

Cf. A004086, A005563, A028504, A061457, A245361.

r:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
select(x-> issqr(r(x)+1), [n^2-1$n=1..10000])[]; # Alois P. Heinz, May 24 2017

Select[Range[0, 10^6], Function[n, Times @@ Boole@ Map[IntegerQ@ Sqrt@ # &, {n + 1, FromDigits@ Reverse@ IntegerDigits@ n + 1}] == 1]] (* Michael De Vlieger, May 24 2017 *)

isok(n) = issquare(n+1) && issquare(fromdigits(Vecrev(digits(n)))+1); \\ Michel Marcus, May 24 2017

A066619 Both n and its reverse are one less than a square.

Original entry on oeis.org

0, 3, 8, 99, 323, 575, 4224, 5775, 9999, 36863, 42024, 999999, 3055503, 3640463, 5597955, 8803088, 32855823, 99999999, 360696063, 422919224, 4227990528, 8250997224, 9999999999, 30485858403, 30536863503, 32154945123

Offset: 1

Erich Friedman, Jan 08 2002

Numbers ending in 0 are not included except 0. - Harry J. Smith, Mar 13 2010

			4227990528 = 65023^2 - 1 and 8250997224 = 90835^2 - 1.

Harry J. Smith, Table of n, a(n) for n = 1..55

Contains A028504.

rev:= proc(x) local L,i;
  L:= convert(x,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(x)
  x mod 10 <> 0 and issqr(rev(x)+1)
end proc:
filter(0):= true:
select(filter, [seq(x^2-1,x=1..10^6)]); # Robert Israel, Nov 08 2023

dtn[L_] := Fold[10#1+#2&, 0, L] A={}; For[i=1, i>0, i++, t=dtn[Reverse[IntegerDigits[i^2-1]]]; If[IntegerQ[(t+1)^(1/2)]&&Mod[i^2, 10]=!=1, AppendTo[A, i^2-1]; Print[A]]]
okQ[n_]:=Module[{idn=IntegerDigits[n]},Last[idn]!=0&& IntegerQ[Sqrt[  FromDigits[ Reverse[idn]]+1]]]; Join[{0},Select[Range[180000]^2-1, okQ]]  (* Harvey P. Dale, Apr 11 2011 *)

Rev(x)= { local(d, r=0); while (x>0, d=x%10; x\=10; r=r*10 + d); return(r) }
{ n=0; for (m=0, 10^10, k=m^2 - 1; if (k%10 && issquare(Rev(k) + 1), if (m==0, k=0); write("b066619.txt", n++, " ", k); if (n==100, return)) ) } \\ Harry J. Smith, Mar 13 2010

More terms from Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

Offset changed from 0 to 1 by Harry J. Smith, Mar 13 2010

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A070254 Perfect squares one more than a palindrome.

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A028503 Numbers k such that k*(k+2) is a palindrome.

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A287389 Both k and its reverse are one less than a square.

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A066619 Both n and its reverse are one less than a square.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions