A241554 Semiprimes generated by the polynomial 2 * n^2 + 29.

1711, 1829, 2077, 2479, 3071, 3901, 5029, 6527, 6757, 7471, 7967, 8479, 10397, 10981, 11581, 14141, 15167, 15517, 15871, 16591, 16957, 17701, 18079, 18847, 19631, 20837, 22927, 23791, 25567, 26941, 27877, 28829, 29797, 30287, 31279, 31781, 32287, 35941, 38117

Offset: 1

Author

K. D. Bajpai, Apr 25 2014

Keywords

• nonn

Comments

2 * n^2 + 29 is a well-known Legendre prime-producing polynomial which generates 29 distinct primes for n = 0, 1, ..., 28. For n = 29, it yields the first semiprime, 1711 = 29 * 59.

The number n = 185 is the least positive integer for which 2*n^2 + 29 = 68479 = 31 * 47 * 47 is not squarefree.

Examples

			2 * 30^2 + 29 = 1829 = 31 * 59, which is a semiprime and is a term.
2 * 35^2 + 29 = 2479 = 37 * 67, which is a semiprime and is a term.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000
• R. A. Mollin, Prime-Producing Quadratics, The American Mathematical Monthly, Vol. 104, No. 6 (Jun. - Jul., 1997), pp. 529-544.

Crossrefs

Cf. A007641 (for primes).

Cf. A001358, A072381, A082919, A145292, A228183, A237627, A353004, A353388.

Programs

Maple

with(numtheory):A241554:= proc() local k; k:=2*x^2+29;if bigomega(k)=2 then RETURN (k); fi; end: seq(A241554(), x=0..500);

Mathematica

A241554 = {}; Do[k = 2 * n^2 + 29; If[PrimeOmega[k] == 2, AppendTo[A241554, k]], {n,200}]; A241554

PARI

s=[]; for(n=1, 200, t=2*n^2+29; if(bigomega(t)==2, s=concat(s, t))); s \\ Colin Barker, Apr 26 2014