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

Author

Patrick De Geest

Keywords

• nonn
• base
• more

Comments

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)

Links

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

Crossrefs

Cf. A027725, A027693, A027722, A027726.

Programs

Mathematica

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 *)

PARI

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

Extensions

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