A070253 -id:A070253 - cp's OEIS frontend

A027719 Numbers k such that k^2 + 1 is a palindrome.

0, 1, 2, 10, 25, 100, 1000, 1020, 1489, 2248, 10000, 10090, 100000, 100910, 102020, 167491, 1000000, 1000200, 1009090, 2744934, 10000000, 10000900, 10090910, 24917195, 100000000, 100909090, 103226660, 271867456, 1000000000, 1000002000, 1009090910, 1577033471

Offset: 1

Patrick De Geest

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, A027720, A002778, A070253.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; Select[Range[0, 10^5], palQ[#^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

A070254 Perfect squares one more than a palindrome.

Original entry on oeis.org

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

A358207 Numbers k such that k^2 + 2 is a palindrome.

Original entry on oeis.org

0, 1, 2, 3, 8, 13, 19, 85, 258, 393, 828, 1811, 2538, 2916, 2986, 3627, 4540, 10503, 140833, 268865, 298436, 423437, 902696, 1050503, 1845571, 2491032, 5513951, 14365940, 25809892, 26237622, 28559254, 61875091, 79094282, 186062629, 246553448, 451977320, 452357920, 620208559, 813448358, 849937635

Offset: 1

Robert Xiao, Nov 04 2022

Cf. A358237, A059100, A027719, A002778, A070253.

isok(k) = my(d=digits(k^2+2)); d == Vecrev(d); \\ Michel Marcus, Nov 04 2022

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A027719 Numbers k such that k^2 + 1 is a palindrome.

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

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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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A358207 Numbers k such that k^2 + 2 is a palindrome.

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