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A109925
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Number of primes of the form n - 2^k.
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14
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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
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OFFSET
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1,4
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COMMENTS
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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 and Robert G. Wilson v, Jul 19 2005
a(A006285(n)) = 0. - Reinhard Zumkeller, May 27 2015
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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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, May 07 2006
G.f.: ( Sum_{i>=0} x^(2^i) ) * ( Sum_{j>=1} x^prime(j) ). - Ilya Gutkovskiy, Feb 10 2022
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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.
127 is the smallest odd number > 1 such that a(n) = 0: A006285(2) = 127. - Reinhard Zumkeller, May 27 2015
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MAPLE
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A109925 := proc(n)
a := 0 ;
for k from 0 do
if n-2^k < 2 then
return a ;
elif isprime(n-2^k) then
a := a+1 ;
end if;
end do:
end proc:
seq(A109925(n), n=1..80) ; # R. J. Mathar, Mar 07 2022
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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}] (* Robert G. Wilson v, Jul 21 2005 *)
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PROG
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(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] ]; // Klaus Brockhaus, Oct 30 2010
(PARI) a(n)=sum(k=0, log(n)\log(2), isprime(n-2^k)) \\ Charles R Greathouse IV, Feb 19 2013
(Haskell)
a109925 n = sum $ map (a010051' . (n -)) $ takeWhile (< n) a000079_list
-- Reinhard Zumkeller, May 27 2015
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CROSSREFS
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Cf. A039669, A109926, A175956, A156695.
Cf. A000079, A000040, A010051, A006285.
Cf. A118954, A118955, A118952, A078687.
Sequence in context: A174314 A237253 A080634 * A306260 A180227 A001468
Adjacent sequences: A109922 A109923 A109924 * 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, Jul 17 2005
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EXTENSIONS
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Corrected and extended by T. D. Noe and Robert G. Wilson v, Jul 19 2005
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STATUS
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approved
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