A235381 Positive numbers n such that n^2 + n + 41 is composite and there are no positive integers c or d such that n = c*d*x^2 + ((d-2)*c + 1)*x + ((41*d^2 - d + 1)*c -1)/d for an integer x.
611, 622, 630, 663, 679, 734, 758, 835, 867, 966, 978, 995, 1006, 1009, 1060, 1088, 1127, 1142, 1157, 1173, 1175, 1183, 1228, 1280, 1345, 1355, 1368, 1388, 1390, 1426, 1433, 1455, 1457, 1467, 1497, 1538, 1539, 1543, 1554, 1578, 1603, 1612, 1613, 1630, 1661
Offset: 1
Keywords
Examples
If d = 1 then n = c*n^2 + (1 - c)*x + 41*c - 1. This is, up to a change of variables, equivalent to A201998.
References
- John Stillwell, Elements of Number Theory, Springer 2003, page 3.
Links
- Matt C. Anderson, Table of n, a(n) for n = 1..75
Crossrefs
Programs
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Maple
maxn := 1000; A := {}; for n to maxn do g := n^2+n+41; if isprime(g) = false then A := `union`(A, {n}) : end if : end do : A: # the A list now contains Positive numbers n such that # n^2 + n + 41 is composite. # an upper limit for the number of iterations in the # triple nested while loops is 1000^3 or a billion. c:=1: d:=1: x:=-1: p:=41: q:=c*d*x^2+((d-2)*c+1)*x+((p*d^2-d+1)*c-1)/d; A2:=A: while q < maxn do while q < maxn do while q < maxn do A2:=A2 minus {q}: A2:=A2 minus {c*x^(2)+(c+1)*x+c*p}: A2:=A2 minus {c*d*x^2-((d-2)*c+1)*x+((p*d^2-d+1)*c-1)/d}: x:=x+1: q:=c*d*x^2+((d-2)*c+1)*x+((p*d^2-d+1)*c-1)/d: end do: c:=c+1: x:=-1: q:=c*d*x^2+((d-2)*c+1)*x+((p*d^2-d+1)*c-1)/d: end do: d:=d+1: c:=1: x:=-1: q:=c*d*x^2+((d-2)*c+1)*x+((p*d^2-d+1)*c-1)/d: end do: A2
Extensions
Corrected and edited by Matt C. Anderson, Jan 23 2014
Comments