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Search: id:A164291
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| A164291 |
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a(n)= p is the first twin prime (p, p+2) for which p+1 has n prime factors (n>=2, multiplicity counted). |
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2
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| 3, 11, 59, 71, 239, 191, 2111, 1151, 14591, 26111, 15359, 139967, 138239, 675839, 2101247, 737279, 4866047, 786431, 22118399, 36175871, 194641919, 63700991, 138412031, 169869311, 1321205759, 11123294207, 16357785599, 4076863487
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OFFSET
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2,1
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COMMENT
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a(3)-a(6) are the first elements of A060213, A102168, A164289, A164290 respectively with n=3,4,5,6 (prime factors in the middle number).
This gives the first p with (p,p+2) twin primes and Omega(p+1)=n with n>=2 (n=1 is impossible).
a(31) = 10871635967. a(32) = 24159191039.
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EXAMPLE
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a(7)=191 because in (191, 192, 193) we have Omega(192)=Omega(2*2*2*2*2*2*3)=7 and 191, 193 are twin primes.
The sequence oscillates and here we see that a(7)<a(6)=239.
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MATHEMATICA
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Omega = If[ # == 1, 0, Apply[Plus, Transpose[FactorInteger[ # ]][[2]]]] &; Wmil = Map[Omega, Range[1, 10000000]]; Aseq=(Flatten@Position[Partition[Wmil, 3, 1], {1, #, 1}])[[1]] & /@ Range[3, 19]
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CROSSREFS
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Cf. A060213, A102168, A164289, A164290.
Sequence in context: A071698 A089188 A086827 this_sequence A137690 A107007 A156560
Adjacent sequences: A164288 A164289 A164290 this_sequence A164292 A164293 A164294
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KEYWORD
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nonn
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Aug 12 2009
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EXTENSIONS
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Definition and comments corrected, a(2) and a(20)-a(29) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 20 2009
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