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 A262228 Deficiency sequence: a(0) = 1, a(n) is the smallest prime p > a(n-1) such that the product of a(i), 1 <= i < n, is deficient (belongs to A005100). 2
 1, 2, 5, 11, 59, 653, 84761, 2763189059, 377406001499268899, 2638619515495963542360422694651593, 135435890329895562961039215198033899386421965445591860752412324961 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The product of the first n+1 terms is the smallest deficient multiple of the product of the first n terms. The product of any finite number of distinct terms of this sequence is deficient. LINKS Amiram Eldar, Table of n, a(n) for n = 0..14 FORMULA a(n) = A151800(floor(1/(2*(Product_{i=2..n-1} a(i)/(a(i)+1))-1)), where A151800 is the "next larger prime" function. Lim_{n->infinity} A001065(Product_{i=0..n} a(i))/(Product_{i=0..n} a(i)) = 1. [Corrected by M. F. Hasler, Dec 04 2017] Conjecture: log(a(n)) ~ e^(an+b) where a and b are approximately 0.6 and -1.6 respectively. EXAMPLE a(3) = 11 because A001065(2*5*7) = A001065(70) = 74 > 70, and A001065(2*5*11) = A001065(110) = 106 < 110. From M. F. Hasler, Dec 14 2017: (Start) Let Q(x) = 1/(2x/sigma(x) - 1), P(n) = Product( a(k), kdefault(primelimit)&&addprimes(p); m*=p); a \\ M. F. Hasler, Dec 14 2017 CROSSREFS Cf. A001065, A005100, A151800 (nextprime). Cf. A002975 (primitive weird numbers), A000203 (sigma), A295001 (same definition but a(0) = 4). Sequence in context: A127010 A140547 A131480 * A213073 A267527 A286453 Adjacent sequences:  A262225 A262226 A262227 * A262229 A262230 A262231 KEYWORD nonn AUTHOR Chayim Lowen, Sep 15 2015 STATUS approved

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)