A072059 Smallest prime p such that 2*p+1 has n distinct prime factors.

2, 7, 97, 577, 7507, 217717, 5232727, 75172597, 1617423307, 59844662377, 2750790860317, 109455887488447, 4621264673452927, 218071376383127767, 10914293640945722527, 662082573402158125717, 41249727342503299116997

Offset: 1

Author

Reinhard Zumkeller, Jun 11 2002

Keywords

• nonn

Comments

Note that for each n=1,...,8, the product of the smallest n-1 distinct prime factors of 2*a(n)+1 is p(n)#/2, where p(n)# is the primorial (A002110) of the n-th prime - and the n-th distinct prime factor >= p(n+1). - Rick L. Shepherd, Jul 06 2002

Examples

			a(4)=577=A000040(106): 2*577+1 = 1155 = 11*7*5*3, 4 distinct factors.
		

Crossrefs

Cf. A001221, A023589, A072055, A072060.

Programs

PARI

for (n=1,8, p=1; until(isprime(p) && omega(2*p+1)==n, p++); print1(p,","))

Extensions

More terms from Rick L. Shepherd, Jul 06 2002

More terms from Don Reble, Apr 15 2003