A368084 Squarefree numbers of the form k^2 + k + 1 such that k^2 + k + 2 is also squarefree.
1, 13, 21, 57, 73, 133, 157, 273, 381, 421, 553, 601, 757, 813, 993, 1261, 1333, 1561, 1641, 1893, 1981, 2257, 2353, 2653, 2757, 3081, 3193, 3541, 3661, 4033, 4161, 5113, 5257, 5701, 5853, 6481, 6973, 7141, 7657, 7833, 8373, 8557, 9121, 9313, 9901, 10101, 10713, 10921
Offset: 1
Examples
1 is a term since 1 is squarefree, 1 = 0^2 + 0 + 1, and 0^2 + 0 + 2 = 2 is also squarefree.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Stoyan Dimitrov, Square-free pairs n^2 + n + 1, n^2 + n + 2, HAL preprint, hal-03735444, 2023; ResearchGate link.
Programs
-
Mathematica
Select[Table[n^2 + n + 1, {n, 0, 100}], And @@ SquareFreeQ /@ {#, #+1} &] -
PARI
lista(kmax) = {my(m); for(k = 0, kmax, m = k^2 + k + 1; if(issquarefree(m) && issquarefree(m + 1), print1(m, ", ")));}
Comments