The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319302 Integers whose binary representation contains a consecutive string of zeros of prime length. 3
 4, 8, 9, 12, 17, 18, 19, 20, 24, 25, 28, 32, 34, 35, 36, 37, 38, 39, 40, 41, 44, 49, 50, 51, 52, 56, 57, 60, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 88, 89, 92, 96, 98, 99, 100, 101, 102, 103, 104, 105, 108, 113, 114, 115, 116, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE 81 = (1010001)_2 is a term because it contains a run of zeros of length 3, and 3 is a prime. 16 = (10000)_2 is not a term because it contains only a run of 4 zeros and 4 is not a prime. MATHEMATICA Select[Range[120], AnyTrue[ Differences@ Flatten@ Position[ IntegerDigits[ 2*# + 1, 2], 1] - 1, PrimeQ] &] (* Giovanni Resta, Sep 17 2018 *) PROG (PARI) is(n) = my(b=binary(n), i=0); for(k=1, #b, if(b[k]==0, i++); if(b[k]==1 || k==#b, if(ispseudoprime(i), return(1), i=0))); 0 \\ Felix Fröhlich, Sep 17 2018 (Python) from re import split from sympy import isprime A319302_list, n = [], 1 while len(A319302_list) < 10000: for d in split('1+', bin(n)[2:]): if isprime(len(d)): A319302_list.append(n) break n += 1 # Chai Wah Wu, Oct 02 2018 CROSSREFS Cf. A004753, A318940. Sequence in context: A244032 A321454 A353834 * A119025 A167903 A074661 Adjacent sequences: A319299 A319300 A319301 * A319303 A319304 A319305 KEYWORD nonn,base,easy AUTHOR W. Zane Billings, Sep 16 2018 EXTENSIONS More terms from Giovanni Resta, Sep 17 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)