A182261 Numbers n such that n^2 + {1,3,7} are semiprimes.

44, 46, 80, 88, 102, 104, 108, 226, 234, 238, 246, 272, 290, 308, 310, 328, 334, 358, 370, 426, 456, 480, 514, 526, 530, 586, 588, 614, 720, 766, 790, 842, 846, 848, 872, 880, 884, 896, 898, 900, 934, 940, 974, 980, 1040, 1076, 1078, 1088, 1110, 1160, 1208

Offset: 1

Author

Jonathan Vos Post, Apr 21 2012

Keywords

• nonn
• easy

Comments

This is to A182238 as A001358 semiprimes are to A000040 primes.

Examples

			44 is in the sequence because (44^2) + 1 = 1937 = 13 * 149, (44^2) + 3 = 1939 = 7 * 277, and  (442) + 7 = 1943 = 29 * 67.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A182238.

Programs

Magma

IsSemiprime:=func; [n: n in [2..1225] | forall{n^2+i: i in [1,3,7] | IsSemiprime(n^2+i)}]; // Bruno Berselli, Apr 22 2012

Maple

a:= proc(n) option remember; local k;
      for k from 1+a(n-1) while map(x-> not isprime(k^2+x) and
          add(i[2], i=ifactors(k^2+x)[2])=2, [1, 3, 7])<>[true$3]
      do od; k
    end: a(0):=0:
seq(a(n), n=1..50);  # Alois P. Heinz, Apr 22 2012

Mathematica

okQ[n_] := AllTrue[n^2 + {1, 3, 7}, PrimeOmega[#] == 2&];
Select[Range[2000], okQ] (* Jean-François Alcover, Jun 01 2022 *)

Formula

{ n : {n^2+1, n^2+3, n^2+7} in A001358 }.