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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001358, A182238.

Sequence in context: A121610 A254752 A178755 * A061757 A342187 A365870

Adjacent sequences: A182258 A182259 A182260 * A182262 A182263 A182264

Keyword

nonn,easy

Author

Jonathan Vos Post, Apr 21 2012

Status

approved