

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.


2



2, 3, 5, 7, 11, 13, 29, 31, 23, 19, 17, 37, 53, 61, 59, 43, 41, 47, 79, 71, 67, 83, 107, 103, 101, 97, 113, 73, 89, 179, 163, 131, 139, 137, 233, 229, 197, 193, 199, 167, 151, 149, 157, 173, 109, 397, 269, 271, 263, 257
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OFFSET

1,1


COMMENTS

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.
Inspired by A059459.


LINKS

Table of n, a(n) for n=1..50.


EXAMPLE

a(1) = 2 = 10_2, by definition, there are no single binary digit primes and this is the least 2bit prime;
a(2) = 3 = 11_2, the least significant bit was "flipped"; all 2bit primes are now present;
a(3) = 5 = 101_2, since the next prime is formed by inserting a 0;
a(4) = 7 = 111_2, since it is obtained by "flipping" the twos bit; all 3bit primes are now present;
a(5) = 11 = 1011_2, since it is the least prime formed by inserting a 0;
a(6) = 13 = 1101_2, since it is the least prime formed by flipping two contiguous bits; all 4bit primes are now present;
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);
a(8) = 31 = 11111_2, since it is the least prime formed by flipping the twos bit;
a(9) = 23 = 10111_2, since it is the least prime formed by flipping one bits;
a(10) = 19 = 10011_2; flip 1 digit;
a(11) = 17 = 10001_2; flip 1 digit, all 5bit primes are now present;
a(12) = 37 = 100101_2; insert the single digit 1, inserting the single digit 0 yields the composite 100001_2 = 33.
a(13) = 53 = 110101_2; flip a single digit; etc.


CROSSREFS

Cf. A000040, A036378, A059459, A292203, A292204.
Sequence in context: A024320 A265885 A294994 * A111252 A181525 A082843
Adjacent sequences: A292202 A292203 A292204 * A292206 A292207 A292208


KEYWORD

base,nonn


AUTHOR

Robert G. Wilson v, Sep 11 2017


STATUS

approved



