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A182261
Numbers n such that n^2 + {1,3,7} are semiprimes.
1
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
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
Sequence in context: A121610 A254752 A178755 * A061757 A342187 A365870
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Apr 21 2012
STATUS
approved