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

1,1

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

Links

Table of n, a(n) for n=1..17.

Example

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

Prog

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

Crossrefs

Cf. A001221, A023589, A072055, A072060.

Sequence in context: A056161 A076740 A112290 * A308961 A240696 A102344

Adjacent sequences: A072056 A072057 A072058 * A072060 A072061 A072062

Keyword

nonn

Author

Reinhard Zumkeller, Jun 11 2002

Extensions

More terms from Rick L. Shepherd, Jul 06 2002

More terms from Don Reble, Apr 15 2003

Status

approved