A027726 -id:A027726 - cp's OEIS frontend

A027724 Numbers k such that k^2+k+8 is a palindrome.

0, 29, 202, 285, 2925, 2935, 20377, 29570, 297119, 2834699, 2837875, 2990390, 2997334, 287010920, 2926428849, 202542945597, 295431039629, 21495814697072, 21614586653852

Offset: 1

Patrick De Geest

From Matthew L. LaSelle, Feb 23 2025: (Start)
k^2+k+8 only ends in a 0, 4, or 8; thus, if it is a palindrome, it only begins and ends in a 4 or 8.
a(20) > 2.174 * 10^13. (End)

Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Cf. A027725, A027693, A027722, A027726.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; f[n_] := n^2 + n + 8; Select[Range[0, 3*10^5], palQ@ f@ # &] (* Giovanni Resta, Aug 29 2018 *)

isok(k) = my(d=digits(k^2+k+8)); d == Vecrev(d); \\ Michel Marcus, Feb 24 2025

a(14)-a(19) from Giovanni Resta, Aug 29 2018

A027727 Palindromes of form k^2 + k + 9.

Original entry on oeis.org

9, 11, 99, 141, 191, 515, 939, 1001, 19191, 90309, 92729, 93339, 109901, 192291, 939939, 1303031, 1997991, 5605065, 9003009, 9887889, 15066051, 97111179, 900030009, 936696639, 5193003915, 11406560411, 13028282031, 15676667651, 16473337461, 90000300009

Offset: 1

Patrick De Geest

Palindromes h such that 4*h - 35 is a square. - Bruno Berselli, Aug 29 2018

Giovanni Resta, Table of n, a(n) for n = 1..71
P. De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Cf. A027726, A027694, A027757, A027758, A027725.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; f[n_] := n^2 + n + 9; Select[f@ Range[0, 10^5], palQ] (* Giovanni Resta, Aug 29 2018 *)
Select[Table[k^2+k+9,{k,0,300000}],PalindromeQ] (* Harvey P. Dale, Nov 21 2024 *)

More terms from Giovanni Resta, Aug 29 2018

cp's OEIS Frontend

A027724 Numbers k such that k^2+k+8 is a palindrome.

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