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A090418
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Number of ways to write n in binary representation as concatenation of primes.
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10
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0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 3, 0, 0, 0, 0, 0, 2, 1, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 3, 0, 2, 2, 4, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 3, 0, 3, 1, 2, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1
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OFFSET
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0,12
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COMMENTS
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a(A090419(n))=0; a(A090420(n))=1; a(A090421(n))>0;
a(A090422(n))=1; a(A090423(n))>1;
a(A090424(n)) = n and a(m) <> n for m < A090424(n).
a(n) = 0 if a = 0 (mod 4); a(n) = a(floor(n/4)) if a = 2 (mod 4). - M. F. Hasler, Apr 21 2015
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
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n=23 -> '10111': '10"111'==2"7, '101"11'==5"3 and '10111'==23,
therefore a(23)=3.
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PROG
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(Haskell)
import Data.List (stripPrefix, unfoldr)
import Data.Maybe (fromJust)
a090418 n = a090418_list !! (n-1)
a090418_list = 0 : f 2 where
f x = (sum $ map g bpss) : f (x + 1) where
g ps | suffix == Nothing = 0
| suffix' == [] = 1
| last suffix' == 0 = 0
| otherwise = a090418 $ fromBits suffix'
where suffix' = fromJust suffix
suffix = stripPrefix ps $ toBits x
bpss = take (fromInteger $ a000720 x) $
map (toBits . fromInteger) a000040_list
toBits = unfoldr
(\u -> if u == 0 then Nothing else Just (mod u 2, div u 2))
fromBits = foldr (\b v -> 2 * v + b) 0
-- Reinhard Zumkeller, Aug 06 2012
(PARI) A090418(n)={ while( n>9 && !bittest(n, 0), bittest(n, 1)||return; n>>=2); n<10 && return(isprime(n)); sum(k=2, #binary(n)-2, if(bittest(n, k-1)&&isprime(n%2^k), A090418(n>>k)), isprime(n))} \\ M. F. Hasler, Apr 21 2015
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CROSSREFS
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Cf. A004676, A007088.
Cf. A191232, A000040.
Cf. A090421, A090423, A257318.
Sequence in context: A116929 A059984 A046675 * A076754 A101659 A074272
Adjacent sequences: A090415 A090416 A090417 * A090419 A090420 A090421
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Nov 30 2003
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EXTENSIONS
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Thanks to Alex Ratushnyak who found an error in A090423, which was the consequence of errors in this sequence; the program was rewritten and data was recomputed by Reinhard Zumkeller, Aug 06 2012
Data in b-file double-checked with independent PARI code. M. F. Hasler, Apr 21 2015
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STATUS
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approved
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