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A215725 Numbers x such that 2*x+1 is prime as is 2*x+3 and x^2+x+41 and (x+1)^2+(x+1)+41. 1

%I

%S 1,2,5,8,14,20,29,35,50,53,68,74,98,113,119,134,230,404,413,509,575,

%T 650,713,725,809,893,935,938,974,1013,1043,1133,1190,1400,1625,1730,

%U 1778,1958,2045,2318,2510,2933,2939,3224,3344,3389,3743,3773

%N Numbers x such that 2*x+1 is prime as is 2*x+3 and x^2+x+41 and (x+1)^2+(x+1)+41.

%C Subsequence of A056561.

%C p=x^2+x+41 and q = (x+1)^2+(x+1)+41, (x+p)^2+x+p+41 = p*q is a semiprime.

%H Pierre CAMI, <a href="/A215725/b215725.txt">Table of n, a(n) for n = 1..1300</a>

%e 1^2+1+41=43=p , 2^2+2+41=47=q , (43+1)^2+(43+1)+41=p*q.

%t Select[Range[4000],And@@PrimeQ[{2#+1,2#+3,#^2+#+41,(#+1)^2+#+42}]&] (* _Harvey P. Dale_, Jun 02 2014 *)

%Y Cf. A056561, A215697.

%K nonn

%O 1,2

%A _Pierre CAMI_, Aug 22 2012

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)