A070254 -id:A070254 - cp's OEIS frontend

A070253 Numbers k such that k^2 - 1 is a palindrome.

1, 2, 3, 10, 18, 24, 65, 76, 100, 192, 205, 1000, 1748, 1908, 2366, 2967, 5732, 10000, 18992, 20565, 100000, 174602, 174748, 179318, 243064, 293787, 552102, 1000000, 1868288, 2967033, 9200157, 10000000, 22765896, 31552660, 93809717, 100000000

Offset: 1

Amarnath Murthy, May 06 2002

Every palindrome of the form h^2-1 is of the form m*(m+2) (easy to prove by replacing h by m+1). In fact this is equal to A028503 + 1. - Patrick De Geest, May 09 2002

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

Cf. A027719, A027720, A070254, A028503.

Do[ If[ a = IntegerDigits[n^2 - 1]; a == Reverse[a], Print[n]], {n, 1, 10^8/4}]
Select[Range[10^8],PalindromeQ[#^2-1]&] (* Harvey P. Dale, Oct 13 2024 *)

intreverse(n)=local(d,rev); rev=0; while(n>0,d=divrem(n,10); n=d[1]; rev=10*rev+d[2]); rev
for(n=1,100000000,q=n*n-1; if(q==intreverse(q),print1(n,",")))

a(n) = A028503(n) + 1. - Giovanni Resta, Aug 29 2018

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

A027720 Palindromes of form k^2 + 1.

Original entry on oeis.org

1, 2, 5, 101, 626, 10001, 1000001, 1040401, 2217122, 5053505, 100000001, 101808101, 10000000001, 10182828101, 10408080401, 28053235082, 1000000000001, 1000400040001, 1018262628101, 7534662664357, 100000000000001, 100018000810001, 101826464628101

Offset: 1

Patrick De Geest

10^(2*m) + 1 for m >= 0 are terms. - Chai Wah Wu, May 25 2017

Giovanni Resta, Table of n, a(n) for n = 1..48
P. De Geest, Palindromic incremented squares of the form n^2+1

Cf. A002522, A027719, A070254, A002779.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; Select[Range[0, 10^5]^2 + 1, palQ] (* Giovanni Resta, Aug 29 2018 *)

a(n) = A027719(n)^2 + 1. - Giovanni Resta, Aug 29 2018

More terms from Giovanni Resta, Aug 28 2018

A028504 Palindromes of form k*(k+2); or palindromes 1 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, 9999999999, 30485858403, 30536863503, 32154945123, 59080108095, 86310801368, 304816618403, 999999999999, 3490500050943

Offset: 1

Patrick De Geest

10^(2*m) - 1 for m > 0 are terms. - Chai Wah Wu, May 25 2017

			4224 belongs to this sequence as 4225 = 65^2.

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, A028503, A002779, A070253, A070254.

stop := 400000; m := 1; while m < stop do s := m*m - 1; if s = int_reverse(s) then write(s," "); end; inc(m); end;

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; Select[Range[10000]^2 - 1, palQ] (* Giovanni Resta, Aug 29 2018 *)
Select[Table[n(n+2),{n,0,19*10^5}],PalindromeQ] (* Harvey P. Dale, Oct 13 2024 *)

a(n) = A028503(n) * (A028503(n) + 2) = A070253(n)^2 - 1 = A070254(n) - 1. - Giovanni Resta, Aug 29 2018

More terms from Giovanni Resta, Aug 28 2018

A358237 Palindromes of the form k^2 + 2.

Original entry on oeis.org

2, 3, 6, 11, 66, 171, 363, 7227, 66566, 154451, 685586, 3279723, 6441446, 8503058, 8916198, 13155131, 20611602, 110313011, 19833933891, 72288388227, 89064046098, 179298892971, 814860068418, 1103556553011, 3406132316043, 6205240425026, 30403655630403, 206380232083602, 666150525051666

Offset: 1

Robert Xiao, Nov 04 2022

Cf. A059100, A358207, A070254, A002779.

Select[Range[0,26*10^6]^2+2,PalindromeQ] (* Harvey P. Dale, Sep 01 2024 *)

cp's OEIS Frontend

A070253 Numbers k such that k^2 - 1 is a palindrome.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A027720 Palindromes of form k^2 + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A028504 Palindromes of form k*(k+2); or palindromes 1 less than a square.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

ARIBAS

Mathematica

Formula

Extensions

A358237 Palindromes of the form k^2 + 2.

Views

Author

Keywords

Crossrefs

Programs

Mathematica