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Search: id:A109925
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| A109925 |
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Number of primes of the form n - 2^k. |
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+0
6
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| 0, 0, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 0, 1, 2, 3, 1, 4, 0, 2, 1, 2, 0, 3, 0, 1, 1, 2, 1, 3, 1, 3, 0, 2, 1, 4, 0, 1, 1, 2, 1, 5, 0, 2, 1, 3, 0, 3, 0, 1, 1, 3, 0, 2, 0, 1, 1, 3, 1, 4, 0, 1, 1, 2, 1, 5, 0, 2, 1, 2, 1, 6, 0, 3, 0, 2, 1, 3, 0, 3, 1, 2, 0, 4, 0, 1, 1, 3, 0, 3, 0, 2, 0, 1, 1, 3, 0, 2, 1, 2, 1, 6
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Erdos conjectures that the numbers in A039669 are the only n for which n-2^r is prime for all 2^r<n. - T. D. Noe (noe(AT)sspectra.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 19 2005
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FORMULA
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a(A118954(n))=0, a(A118955(n))>0; A118952(n)<=a(n); A078687(n)=a(A000040(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 07 2006
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EXAMPLE
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a(21) = 4, 21-2 =19, 21-4 = 17, 21-8 = 13, 21-16 = 5, four primes.
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MATHEMATICA
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Table[cnt=0; r=1; While[r<n, If[PrimeQ[n-r], cnt++ ]; r=2r]; cnt, {n, 150}] (Noe)
f[n_] := Count[ PrimeQ[n - 2^Range[0, Floor[ Log[2, n]]]], True]; Table[ f[n], {n, 105}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 21 2005)
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CROSSREFS
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Cf. A109926.
Sequence in context: A049710 A025143 A080634 this_sequence A001468 A014675 A107362
Adjacent sequences: A109922 A109923 A109924 this_sequence A109926 A109927 A109928
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 17 2005
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 19 2005
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