cp's OEIS Frontend

A292205 A sequence of primes beginning with 2, with each prime after that being the smallest prime not present differing by the least number of contiguous bits.

%I A292205 #32 Nov 22 2017 19:04:22
%S A292205 2,3,5,7,11,13,29,31,23,19,17,37,53,61,59,43,41,47,79,71,67,83,107,
%T A292205 103,101,97,113,73,89,179,163,131,139,137,233,229,197,193,199,167,151,
%U A292205 149,157,173,109,397,269,271,263,257
%N A292205 A sequence of primes beginning with 2, with each prime after that being the smallest prime not present differing by the least number of contiguous bits.
%C A292205 Least prime not already present, formed from the previous prime by first flipping or inverting a single binary bit and if no such prime exists, then two contiguous bits, then three, etc., and if no such prime exists then by inserting increasing binary bits starting with "0", "1", "00", "01", "10", "11", etc. resulting in the least prime so created. Leading zeros are forbidden.
%C A292205 Inspired by A059459.
%e A292205 a(1) =  2 =     10_2, by definition, there are no single binary digit primes and this is the least 2-bit prime;
%e A292205 a(2) =  3 =     11_2, the least significant bit was "flipped"; all 2-bit primes are now present;
%e A292205 a(3) =  5 =    101_2, since the next prime is formed by inserting a 0;
%e A292205 a(4) =  7 =    111_2, since it is obtained by "flipping" the twos bit; all 3-bit primes are now present;
%e A292205 a(5) = 11 =   1011_2, since it is the least prime formed by inserting a 0;
%e A292205 a(6) = 13 =   1101_2, since it is the least prime formed by flipping two contiguous bits; all 4-bit primes are now present;
%e A292205 a(7) = 29 =  11101_2, since it is the least prime formed by inserting a 1; no prime is generated by the insertion of a 0, i.e.; from 1101 (13_10) -> 10101 (21_10) or 11001 (25_10);
%e A292205 a(8) = 31 =  11111_2, since it is the least prime formed by flipping the twos bit;
%e A292205 a(9) = 23 =  10111_2, since it is the least prime formed by flipping one bits;
%e A292205 a(10) = 19 =  10011_2; flip 1 digit;
%e A292205 a(11) = 17 =  10001_2; flip 1 digit, all 5-bit primes are now present;
%e A292205 a(12) = 37 = 100101_2; insert the single digit 1, inserting the single digit 0 yields the composite 100001_2 = 33.
%e A292205 a(13) = 53 = 110101_2; flip a single digit; etc.
%Y A292205 Cf. A000040, A036378, A059459, A292203, A292204.
%K A292205 base,nonn
%O A292205 1,1
%A A292205 _Robert G. Wilson v_, Sep 11 2017