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 A171000 Irreducible Boolean polynomials written as binary vectors. 6
 1, 10, 11, 101, 1001, 1011, 1101, 10001, 10011, 10111, 11001, 11101, 100001, 100011, 100101, 100111, 101001, 101011, 110001, 110101, 111001, 1000001, 1000011, 1000101, 1000111, 1001011, 1001101, 1001111, 1010001, 1010011, 1010111, 1011001, 1011101, 1100001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are the polynomials enumerated in A169912, and written in base 10 in A067139. This sequence consists of 1 and the lunar primes in base 2 arithmetic. To construct the lunar base 2 primes, start with 10, and repeatedly adjoin the next smallest binary number that is not a lunar base-2 multiple of any earlier number. - N. J. A. Sloane, Jan 26 2011 LINKS N. J. A. Sloane, Table of n, a(n) for n = 1..5655 D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing] PROG (Python) def addn(m1, m2): s1, s2 = "{0:b}".format(m1), "{0:b}".format(m2) len_max = max(len(s1), len(s2)) return int(''.join(max(i, j) for i, j in zip(s1.rjust(len_max, '0'), s2.rjust(len_max, '0')))) def muln(m1, m2): s1, s2, prod = "{0:b}".format(m1), "{0:b}".format(m2), '0' for i in range(len(s2)): k = s2[-i-1] prod = addn(int(str(prod), 2), int(''.join(min(j, k) for j in s1), 2)*2**i) return prod L_p10, m = [1], 2 while m < 100: ct = 0 for i in range(1, len(L_p10)): p = L_p10[i] for j in range(2, m): jp = int(str(muln(j, p)), 2) if jp > m: break if jp == m: ct += 1; break if ct > 0: break if ct == 0: L_p10.append(m) m += 1 L_p2 = [] for d in L_p10: L_p2.append("{0:b}".format(d)) print(*L_p2, sep =', ') # Ya-Ping Lu, Dec 27 2020 CROSSREFS Cf. A169912, A067139. Base 3 lunar primes: A130206, A170806. Sequence in context: A305379 A004685 A361335 * A346821 A222365 A041216 Adjacent sequences: A170997 A170998 A170999 * A171001 A171002 A171003 KEYWORD nonn AUTHOR N. J. A. Sloane, Aug 31 2010 STATUS approved

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