login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A217302 Minimal natural number (in decimal representation) with n prime substrings in binary representation (substrings with leading zeros are considered to be nonprime). 24
1, 2, 5, 7, 11, 15, 27, 23, 31, 55, 47, 63, 111, 95, 187, 127, 223, 191, 381, 255, 447, 503, 383, 511, 1015, 895, 767, 1023, 1533, 1791, 1535, 1919, 3039, 3069, 3067, 3839, 3967, 6079, 6139, 6135, 7679, 8063, 8159, 12159, 12271, 15359, 16127 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence is well-defined in that for each n the set of numbers with n prime substrings in binary representation is not empty. Proof: A000975(n+1) has exactly n prime substrings in binary representation (s. A000975).

All terms with n > 1 are odd.

LINKS

Hieronymus Fischer, Table of n, a(n) for n = 0..300

FORMULA

a(n) >= 2^ceiling(sqrt(8*n+1)-1)/2).

a(n) <= A000975(n+1).

a(n+1) <= 2*a(n)+1.

EXAMPLE

a(1) = 2 = 10_2, since 2 is the least number with 1 prime substring (=10_2) in binary representation.

a(2) = 5 = 101_2, since 5 is the least number with 2 prime substrings in binary representation (10_2 and 101_2).

a(4) = 11 = 1011_2, since 11 is the least number with 4 prime substrings in binary representation (10_2, 11_2, 101_2 and 1011_2).

a(8) = 31 = 11111_2, since 31 is the least number with 8 prime substrings in binary representation (4 times 11_2, 3 times 111_2, and 11111_2).

a(9) = 47 = 101111_2, since 47 is the least number with 9 prime substrings in binary representation (10_2, 3 times 11_2, 101_2, 2 times 111_2, 1011_2, and 10111_2).

CROSSREFS

Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684, A211685, A035244, A079397, A213300-A213321, A217303-A217309, A000975.

Sequence in context: A084935 A239072 A317242 * A062409 A089781 A144832

Adjacent sequences:  A217299 A217300 A217301 * A217303 A217304 A217305

KEYWORD

nonn,base

AUTHOR

Hieronymus Fischer, Nov 22 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 08:58 EDT 2018. Contains 316433 sequences. (Running on oeis4.)