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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 (list; graph; refs; listen; history; text; internal format)
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: A254752 A063837 A178755 * A061757 A342187 A088066

Adjacent sequences: A182258 A182259 A182260 * A182262 A182263 A182264

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Apr 21 2012

STATUS

approved

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Last modified February 2 02:30 EST 2023. Contains 359997 sequences. (Running on oeis4.)