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 A305473 Let k be a Sierpiński or Riesel number divisible by 2*n - 1, and let p be the largest number in a set of primes which cover every number of the form k*2^m + 1 (or of the form k*2^m - 1) with m >= 1. a(n) = p if and only if there exists no number k that has a covering set with largest prime < p. 2
 73, 257, 151, 151, 257, 73, 151, 1321, 73, 109, 1321, 73, 151, 257, 73, 73, 331, 257, 109, 331, 73, 73, 1321, 73, 151, 331, 73, 241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS R. G. Stanton found that a(2) = 257. a(n) >= 73 for any n, see [Stanton]. There exists infinitely many Riesel numbers that are divisible by 15. The number 334437671621489828385689959795356586832846847109919809460835 is one such number. REFERENCES R. G. Stanton, Further results on covering integers of the form 1 + k * 2^n by primes, pp. 107-114 in: Kevin L. McAvaney (ed.), Combinatorial Mathematics VIII, Lecture Notes in Mathematics 884, Berlin: Springer, 1981. LINKS Carlos Rivera, Problem 49. Sierpinski-like numbers, The Prime Puzzles and Problems Connection. FORMULA a(((2*n-1)^b+1)/2) = a(n) for every b >= 2. a((2*b-1)*n-b+1) >= a(n) for every b >= 2; n > 1. a(n) = 73 if and only if gcd(2*n-1, 70050435) = 1. EXAMPLE Examples of the covering sets: - for n = 2, the set is {5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257}, - for n = 3, the set is {3, 7, 11, 13, 19, 31, 37, 41, 61, 73, 109, 151}, - for n = 4, the set is {3, 5, 11, 13, 19, 31, 37, 41, 61, 73, 151}, - for n = 6, the set is {3, 5, 7, 13, 19, 37, 73}, - for n = 7, the set is {3, 5, 7, 11, 19, 31, 37, 41, 61, 73, 151}, - for n = 8, the set is {7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 61, 71, 73, 97, 109, 113, 127, 151, 193, 211, 241, 257, 281, 331, 337, 421, 433, 577, 673, 1153, 1321}, - for n = 11, the set is {5, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 181, 193, 241, 257, 331, 433, 577, 631, 673, 1153, 1321}, - for n = 17, the set is {5, 7, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331}, - for n = 18, the set is {3, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257}, - for n = 20, the set is {5, 7, 11, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331}, - for n = 26, the set is {5, 7, 11, 13, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331}, - for n = 28, the set is {3, 7, 13, 17, 19, 37, 73, 109, 241}. CROSSREFS Cf. A076336, A101036, A187714, A187716, A213529, A222534, A244071, A244562, A306151. Sequence in context: A201715 A337848 A071392 * A142434 A128032 A142489 Adjacent sequences:  A305470 A305471 A305472 * A305474 A305475 A305476 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Jun 02 2018 STATUS approved

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Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)