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Search: id:A072059
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| A072059 |
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Smallest prime p such that 2*p+1 has n distinct prime factors. |
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+0
3
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| 2, 7, 97, 577, 7507, 217717, 5232727, 75172597, 1617423307, 59844662377, 2750790860317, 109455887488447, 4621264673452927, 218071376383127767, 10914293640945722527, 662082573402158125717, 41249727342503299116997
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (rshepherd2(AT)hotmail.com), Jul 06 2002
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EXAMPLE
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a(4)=577=A000040(106): 2*577+1 = 1155 = 11*7*5*3, 4 distinct factors.
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PROGRAM
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(PARI) for (n=1, 8, p=1; until(isprime(p) && omega(2*p+1)==n, p++); print1(p, ", "))
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CROSSREFS
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Cf. A001221, A023589, A072055, A072060.
Sequence in context: A056161 A076740 A112290 this_sequence A102344 A087589 A002812
Adjacent sequences: A072056 A072057 A072058 this_sequence A072060 A072061 A072062
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 11 2002
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EXTENSIONS
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More terms from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 06 2002
More terms from Don Reble (djr(AT)nk.ca), Apr 15 2003
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