A088148 Least number which when rotated through all its binary places produces n primes, not counting any repeats.

2, 5, 11, 43, 158, 2143, 2302, 2558, 36542, 548543, 711679, 786431, 9010423, 10452461, 10065788911, 34481371903

Offset

1,1

Comments

It is probably not the case that this always produces the same bit cycle as A088149. - Franklin T. Adams-Watters, Mar 29 2014

Links

Table of n, a(n) for n=1..16.

Example

a(5) = 158 because 158 in base two is 10011110. This will produce eight possible new numbers; 00111101 = 61, 01111010 = 122, 11110100 = 244, 11101001 = 233, 11010011 = 211, 10100111 = 167, 01001111 = 79 and back to the beginning 10011110 = 158. Of those eight numbers (61, 122, 244, 233, 211, 167, 79 & 158) only five of them are primes. Notice that this is the same bit cycle as in A088149 but rotated differently.

Mathematica

f[n_] := Count[ PrimeQ[ Union[ Table[ FromDigits[ RotateLeft[ IntegerDigits[n, 2], i], 2], {i, 1, Floor[ Log[2, n] + 1]}]]], True]; a = Table[0, {15}]; k = 1; Do[c = f[k]; If[c < 100 && a[[c+1]] == 0, a[[c+1]] = n]; k++, {n, 1, 10^7}]; a

Prog

(Python)
from itertools import count
from sympy import isprime
def A088148(n):
    if n == 1: return 2
    for p in count((1<<n)-1):
        if p.bit_count() >= n:
            m = p.bit_length()
            l = 1<<m-1
            k, cset, q = l-1, set(), p
            for _ in range(m):
                if p not in cset and isprime(p):
                    cset.add(p)
                p = bool(p&l)+((p&k)<<1)
            if len(cset) == n:
                return q # Chai Wah Wu, Jan 23 2023

Crossrefs

Cf. A088149.

Sequence in context: A071313 A172297 A128231 * A088149 A153989 A160859

Adjacent sequences: A088145 A088146 A088147 * A088149 A088150 A088151

Keyword

nonn,base,more

Author

Robert G. Wilson v, Sep 19 2003

Extensions

Edited by Franklin T. Adams-Watters, Mar 29 2014

a(15) from Chai Wah Wu, Jan 24 2023

a(16) from Chai Wah Wu, Jan 27 2023

Status

approved