A292203 -id:A292203 - cp's OEIS frontend

A292204 Primes as they appear in A006068.

3, 2, 7, 5, 13, 11, 31, 29, 17, 19, 23, 61, 59, 53, 37, 47, 41, 43, 127, 113, 97, 103, 101, 109, 107, 67, 71, 79, 73, 89, 83, 251, 241, 227, 229, 239, 233, 193, 199, 197, 223, 211, 131, 137, 139, 157, 151, 149, 191, 179, 181, 163, 167, 173, 509, 499, 503, 487, 491, 449, 463, 461

Offset: 1

Robert G. Wilson v, Sep 11 2017

nonn

a(n) is the i-th prime (as it appears in A000040) for i = 2, 1, 4, 3, 6, 5, 9, 10, 11, 8, 7, 15, 17, 18, 16, 14, etc.

Cf. A006068, A292203, A292205.

f[n_] := BitXor @@ Table[ Floor[n/2^m], {m, 0, Floor[Log2@ n]}]; Select[ Array[f, 300], PrimeQ]

grayinto(n) = my(B=n); for(k=1, log(n+1)\log(2), B=bitxor(B, n\2^k)); B;
lista(nn) = for (n=1, nn, if (isprime(p=grayinto(n)), print1(p, ", "))); \\ Michel Marcus, Oct 10 2017

from itertools import count, islice
from sympy import isprime
def A292204_gen(): # generator of terms
    for n in count(0):
        k, m = n, n>>1
        while m > 0:
            k ^= m
            m >>= 1
        if isprime(k):
            yield k
A292204_list = list(islice(A292204_gen(),30)) # Chai Wah Wu, Jun 29 2022

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.

Original entry on oeis.org

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

Offset: 1

Robert G. Wilson v, Sep 11 2017

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.

			a(1) =  2 =     10_2, by definition, there are no single binary digit primes and this is the least 2-bit prime;
a(2) =  3 =     11_2, the least significant bit was "flipped"; all 2-bit 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 3-bit 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 4-bit 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 5-bit 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.

Cf. A000040, A036378, A059459, A292203, A292204.

cp's OEIS Frontend

A292204 Primes as they appear in A006068.

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