A027757 -id:A027757 - cp's OEIS frontend

A027726 Numbers k such that k^2+k+9 is a palindrome.

0, 1, 9, 11, 13, 22, 30, 31, 138, 300, 304, 305, 331, 438, 969, 1141, 1413, 2367, 3000, 3144, 3881, 9854, 30000, 30605, 72062, 106801, 114141, 125206, 128348, 300000, 315165, 963304, 980560, 989154, 2378507, 3000000, 3040604, 3045679, 3152290, 3932806

Offset: 1

Patrick De Geest

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. A027727, A027694, A027757, A027758, A027724.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; f[n_] := n^2 + n + 9; Select[Range[0, 3*10^5], palQ@ f@ # &]

More terms 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

A174152 Primes p such that p^2+p+9 is also prime.

Original entry on oeis.org

13, 19, 43, 79, 139, 151, 211, 271, 373, 433, 523, 643, 739, 751, 769, 853, 919, 1033, 1051, 1093, 1129, 1171, 1423, 1429, 1471, 1531, 1579, 1663, 1741, 1759, 1789, 1933, 2053, 2281, 2389, 2521, 2689, 2731, 2749, 2833, 3061, 3109, 3163, 3271, 3313, 3319

Offset: 1

Vincenzo Librandi, Mar 10 2010

			For p=13, 13^2+13+9=191; p=19, 19^2+19+9=389; p=43, 43^2+43+9=1901.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A027757.

Subsequence of A002476.

[p: p in PrimesUpTo(10000) | IsPrime(p^2+p+9)];

Select[Prime[Range[500]], PrimeQ[#^2 + # + 9]&] (* Vincenzo Librandi, Apr 16 2013 *)

A027757 INTERSECT A000040. [From R. J. Mathar, Jul 06 2010]

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A027726 Numbers k such that k^2+k+9 is a palindrome.

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

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A174152 Primes p such that p^2+p+9 is also prime.

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