cp's OEIS Frontend

A217302 Minimal natural number (in decimal representation) with n prime substrings in binary representation (substrings with leading zeros are considered to be nonprime).

%I A217302 #15 Dec 16 2018 23:47:35
%S A217302 1,2,5,7,11,15,27,23,31,55,47,63,111,95,187,127,223,191,381,255,447,
%T A217302 503,383,511,1015,895,767,1023,1533,1791,1535,1919,3039,3069,3067,
%U A217302 3839,3967,6079,6139,6135,7679,8063,8159,12159,12271,15359,16127
%N A217302 Minimal natural number (in decimal representation) with n prime substrings in binary representation (substrings with leading zeros are considered to be nonprime).
%C A217302 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 (see A000975).
%C A217302 All terms with n > 1 are odd.
%H A217302 Hieronymus Fischer, <a href="/A217302/b217302.txt">Table of n, a(n) for n = 0..300</a>
%F A217302 a(n) >= 2^ceiling(sqrt(8*n+1)-1)/2).
%F A217302 a(n) <= A000975(n+1).
%F A217302 a(n+1) <= 2*a(n)+1.
%e A217302 a(1) = 2 = 10_2, since 2 is the least number with 1 prime substring (=10_2) in binary representation.
%e A217302 a(2) = 5 = 101_2, since 5 is the least number with 2 prime substrings in binary representation (10_2 and 101_2).
%e A217302 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).
%e A217302 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).
%e A217302 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).
%Y A217302 Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684, A211685, A035244, A079397, A213300-A213321, A217303-A217309, A000975.
%K A217302 nonn,base
%O A217302 0,2
%A A217302 _Hieronymus Fischer_, Nov 22 2012