A027754 -id:A027754 - cp's OEIS frontend

A027755 Primes of the form k^2 + k + 5.

5, 7, 11, 17, 47, 61, 137, 277, 311, 347, 467, 557, 761, 997, 1061, 1487, 1811, 2357, 2657, 3911, 4561, 5261, 5407, 5857, 6011, 6977, 7487, 8377, 8747, 9511, 11777, 12437, 13577, 14767, 16007, 17827, 18637, 18911, 21467, 23567, 25127

Offset: 1

Patrick De Geest

nonn

a(5) through a(14) are identical to the first 10 values of q, the left-hand column of "Example 2.3. We give examples of maximal and minimal elliptic curves over finite fields over F_q with discriminant -19 for all q < 1000", p. 4, and "Example 5.2. We produce examples of optimal curves over finite fields with discriminant -19" pp. 10-11 of E. Alekseenko, et al. - Jonathan Vos Post, Feb 12 2009

Seiichi Manyama, Table of n, a(n) for n = 1..10000
E. Alekseenko, S. Aleshnikov, N. Markin and A. Zaytsev, Optimal Curves of Genus 3 over Finite Fields with Discriminant -19, arXiv:0902.1901 [math.AG], 2009-2011.
P. De Geest, World!Of Numbers

Cf. A014556, A027754.

[a: n in [0..250]|IsPrime(a) where a is n^2+n+5]; // Vincenzo Librandi, Dec 20 2010

nn = Range[0, 200]; Select[nn^2 + nn + 5, PrimeQ] (* Jean-François Alcover, Nov 17 2018 *)

a(n) = A027754(n)^2 + A027754(n) + 5. - Seiichi Manyama, Mar 19 2017

a(n) >> n^2 log n (Brun sieve). - Charles R Greathouse IV, Nov 01 2022

A027718 Numbers k such that k^2+k+5 is a palindrome.

Original entry on oeis.org

0, 1, 2, 8, 12, 26, 74, 127, 224, 230, 2751, 3462, 4012, 4067, 12752, 22424, 27548, 28168, 105322, 107422, 2358150, 2724718, 2775383, 4063892, 7569245, 85125933, 87579753, 106617617, 2237334999, 2426472519, 2765569146, 2781875716, 2815069131, 4029203527

Offset: 1

Patrick De Geest

Giovanni Resta, Table of n, a(n) for n = 1..46

Cf. A027728, A027690, A027754, A027755, A027716, A027729.

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

More terms from Giovanni Resta, Aug 28 2018

A027728 Palindromes of form k^2 + k + 5.

Original entry on oeis.org

5, 7, 11, 77, 161, 707, 5555, 16261, 50405, 53135, 7570757, 11988911, 16100161, 16544561, 162626261, 502858205, 758919857, 793464397, 11092829011, 11539593511, 5560873780655, 7424090904247, 7702753572077, 16515222251561, 57293477439275, 7246424554246427

Offset: 1

Patrick De Geest

Giovanni Resta, Table of n, a(n) for n = 1..46
P. De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Cf. A027718, A027690, A027754, A027755, A027717, A027728, A027721.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; f[n_] := n^2 + n + 5; Select[f@ Range[0, 10^5], palQ] (* Giovanni Resta, Aug 29 2018 *)
Select[Table[k^2+k+5,{k,0,852*10^5}],PalindromeQ] (* Harvey P. Dale, Aug 04 2025 *)

More terms from Giovanni Resta, Aug 28 2018

cp's OEIS Frontend

A027755 Primes of the form k^2 + k + 5.

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A027718 Numbers k such that k^2+k+5 is a palindrome.

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A027728 Palindromes of form k^2 + k + 5.

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