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%I #29 Jan 27 2023 09:55:07
%S 2,5,11,43,158,2143,2302,2558,36542,548543,711679,786431,9010423,
%T 10452461,10065788911,34481371903
%N Least number which when rotated through all its binary places produces n primes, not counting any repeats.
%C It is probably not the case that this always produces the same bit cycle as A088149. - _Franklin T. Adams-Watters_, Mar 29 2014
%e 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.
%t 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
%o (Python)
%o from itertools import count
%o from sympy import isprime
%o def A088148(n):
%o if n == 1: return 2
%o for p in count((1<<n)-1):
%o if p.bit_count() >= n:
%o m = p.bit_length()
%o l = 1<<m-1
%o k, cset, q = l-1, set(), p
%o for _ in range(m):
%o if p not in cset and isprime(p):
%o cset.add(p)
%o p = bool(p&l)+((p&k)<<1)
%o if len(cset) == n:
%o return q # _Chai Wah Wu_, Jan 23 2023
%Y Cf. A088149.
%K nonn,base,more
%O 1,1
%A _Robert G. Wilson v_, Sep 19 2003
%E Edited by _Franklin T. Adams-Watters_, Mar 29 2014
%E a(15) from _Chai Wah Wu_, Jan 24 2023
%E a(16) from _Chai Wah Wu_, Jan 27 2023
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