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, 2, 5, 8, 14, 20, 29, 35, 50, 53, 68, 74, 98, 113, 119, 134, 230, 404, 413, 509, 575, 650, 713, 725, 809, 893, 935, 938, 974, 1013, 1043, 1133, 1190, 1400, 1625, 1730, 1778, 1958, 2045, 2318, 2510, 2933, 2939, 3224, 3344, 3389, 3743, 3773

Offset: 1

Author

Pierre CAMI, Aug 22 2012

Keywords

• nonn

Comments

Subsequence of A056561.

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

Examples

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

Links

• Pierre CAMI, Table of n, a(n) for n = 1..1300

Crossrefs

Cf. A056561, A215697.

Programs

Mathematica

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