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 A329245 For any n > 0, let m = 2*n - 1 (m is the n-th odd number); a(n) is the least k > 1 such that m AND (m^k) = m (where AND denotes the bitwise AND operator). 1
 2, 3, 3, 3, 3, 5, 5, 3, 3, 7, 7, 5, 5, 9, 9, 3, 3, 3, 11, 3, 3, 5, 5, 5, 5, 15, 7, 9, 9, 17, 17, 3, 3, 3, 5, 5, 5, 5, 9, 3, 3, 23, 7, 13, 13, 9, 9, 5, 5, 19, 11, 3, 3, 5, 21, 9, 9, 15, 23, 17, 17, 33, 33, 3, 3, 3, 3, 3, 7, 5, 5, 3, 3, 7, 7, 21, 21, 17, 9, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is well defined: for any n > 0: - let x be such that 2*n-1 < 2^x, - hence gcd(2*n-1, 2^x) = 1, - and a(n) <= 1 + ord_{2^x}(2*n-1) (where ord_u(v) is the multiplicative order of v modulo u). LINKS Rémy Sigrist, Table of n, a(n) for n = 1..8192 EXAMPLE For n = 7: - m = 2*7 - 1 = 13, - 13 AND (13^2) = 9, - 13 AND (13^3) = 5, - 13 AND (13^4) = 1, - 13 AND (13^5) = 13, - hence a(7) = 5. PROG (PARI) a(n) = my (m=2*n-1, mk=m); for (k=2, oo, if (bitand(m, mk*=m)==m, return (k))) CROSSREFS Cf. A253719. Sequence in context: A257246 A056206 A257245 * A155047 A029088 A253591 Adjacent sequences:  A329242 A329243 A329244 * A329246 A329247 A329248 KEYWORD nonn,base AUTHOR Rémy Sigrist, Nov 09 2019 STATUS approved

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Last modified October 20 15:17 EDT 2021. Contains 348111 sequences. (Running on oeis4.)