A175281 -id:A175281 - cp's OEIS frontend

A175282 Positive numbers n with property that n^2+3n+9 is prime (A005471).

1, 2, 4, 7, 8, 10, 11, 16, 17, 23, 25, 28, 29, 31, 32, 37, 38, 43, 49, 50, 56, 58, 64, 70, 73, 85, 88, 91, 94, 95, 98, 101, 107, 112, 121, 122, 127, 130, 133, 134, 136, 140, 142, 143, 155, 158, 163, 164, 169, 172, 175, 176, 179, 182, 197, 200, 205, 206, 212, 214, 218

Offset: 1

Zak Seidov, Mar 21 2010

nonn

Notice that at n=-1, n^2+3n+9=7 is also (positive) prime.

Erik Dofs, Solutions of x^3+y^3+z^3=n*x*y*z, Acta Arithm. 73.3 (1995) 201

Cf. A005471, A175281.

A175282 := proc(n)
    option remember;
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            if isprime(a^2+3*a+9) then
                return a;
            end if;
        end do;
    end if;
end proc: # R. J. Mathar, Jun 06 2019

Select[Range[1,400],PrimeQ[ #^2+3*#+9]&]

A175283 Numbers k with the property that k and k^2 + 3k+9 are primes.

Original entry on oeis.org

2, 7, 11, 17, 23, 29, 31, 37, 43, 73, 101, 107, 127, 163, 179, 197, 239, 277, 281, 317, 331, 359, 367, 421, 457, 463, 487, 541, 569, 613, 617, 619, 661, 709, 739, 773, 787, 809, 823, 877, 941, 947, 953, 991, 1019, 1031, 1033, 1039, 1051, 1087, 1163, 1187

Offset: 1

Zak Seidov, Mar 21 2010

nonn

Or, primes in A175282.

Cf. A005471, A175281, A175282.

[ n: n in [0..1250] | IsPrime(n) and IsPrime(n^2+3*n+9)] // Vincenzo Librandi, Jan 30 2011

Select[Prime[Range[400]],PrimeQ[ #^2+3*#+9]&]

A175284 Primes p of the form p=n^2+3n+9 such that q=p^2+3p+9 is also prime.

Original entry on oeis.org

7, 37, 163, 709, 877, 46447, 67867, 81517, 118687, 238639, 292147, 331207, 430999, 497737, 548347, 628063, 1120429, 1412539, 1462897, 1655089, 1680919, 1955809, 2642257, 3205897, 3358063, 3394813, 3781087, 4654813, 4715419, 4745869

Offset: 1

Zak Seidov, Mar 21 2010

nonn

Intersection of A175283 and A005471.

Cf. A005471, A175281-3.

Reap[Do[If[PrimeQ[p=n^2+3n+9]&&PrimeQ[q=p^2+3p+9],Sow[p]],{n,-1,10^4}]][[2,1]]

A175285 Numbers n with property that 42*n+37 is in A175284.

Original entry on oeis.org

0, 3, 16, 20, 1105, 1615, 1940, 2825, 5681, 6955, 7885, 10261, 11850, 13055, 14953, 26676, 33631, 34830, 39406, 40021, 46566, 62910, 76330, 79953, 80828, 90025, 110828, 112271, 112996, 116340, 126116, 153065, 165126, 175828, 205030, 218953

Offset: 0

Zak Seidov, Mar 21 2010

nonn

Except of the first term in A175284, all terms == 37 mod 42.

Cf. A005471, A175281-4.

cp's OEIS Frontend

A175282 Positive numbers n with property that n^2+3n+9 is prime (A005471).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A175283 Numbers k with the property that k and k^2 + 3k+9 are primes.

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

A175284 Primes p of the form p=n^2+3n+9 such that q=p^2+3p+9 is also prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A175285 Numbers n with property that 42*n+37 is in A175284.

Views

Author

Keywords

Comments

Crossrefs