A027719 -id:A027719 - 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

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

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

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A027720 Palindromes of form k^2 + 1.

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A070254 Perfect squares one more than a palindrome.

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

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