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A090418 Number of ways to write n in binary representation as concatenation of primes. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 (corrected by Georg Fischer, Jan 20 2019)

EXAMPLE

n=23 -> '10111': '10"111'==2"7, '101"11'==5"3 and '10111'==23,

therefore a(23)=3.

PROG

(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

CROSSREFS

Cf. A004676, A007088.

Cf. A191232, A000040.

Cf. A090421, A090423, A257318.

Sequence in context: A059984 A046675 A275949 * A322452 A076754 A339933

Adjacent sequences:  A090415 A090416 A090417 * A090419 A090420 A090421

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Nov 30 2003

EXTENSIONS

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

STATUS

approved

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Last modified April 14 21:21 EDT 2021. Contains 342962 sequences. (Running on oeis4.)