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A109925
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Number of primes of the form n - 2^k.
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7
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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; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
| 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
| a(21) = 4, 21-2 =19, 21-4 = 17, 21-8 = 13, 21-16 = 5, four primes.
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MATHEMATICA
| 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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PROG
| (MAGMA) a109925:=function(n); count:=0; e:=1; while e le n do if IsPrime(n-e) then count+:=1; end if; e*:=2; end while; return count; end function; [ a109925(n): n in [1..105] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 30 2010]
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CROSSREFS
| Cf. A109926.
Cf. A175956. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 30 2010]
Sequence in context: A025143 A174314 A080634 * A180227 A001468 A014675
Adjacent sequences: A109922 A109923 A109924 * A109926 A109927 A109928
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KEYWORD
| easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 17 2005
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EXTENSIONS
| 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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