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 A108540 Golden semiprimes: a(n)=p*q and abs(p*phi-q)<1, where phi = golden ratio = (1+sqrt(5))/2. 17
 6, 15, 77, 187, 589, 851, 1363, 2183, 2747, 7303, 10033, 15229, 16463, 17201, 18511, 27641, 35909, 42869, 45257, 53033, 60409, 83309, 93749, 118969, 124373, 129331, 156433, 201563, 217631, 232327, 237077, 255271, 270349, 283663, 303533, 326423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = A108541(n)*A108542(n) = A000040(k)*A108539(k) for some k. REFERENCES Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176.  Solution published in Vol. 12, No. 1, Winter 2000, pp. 61-62. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe) Eric Weisstein's World of Mathematics, Golden Ratio Eric Weisstein's World of Mathematics, Semiprime EXAMPLE 589 = 19*31 and abs(19*phi - 31) = abs(30,7426... - 31) < 1, therefore 589 is a term. MATHEMATICA f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p=1; Do[p = NextPrime[p]; q = f[p]; If[q > 0, AppendTo[seq, p*q]], {100}]; seq (* Amiram Eldar, Nov 28 2019 *) CROSSREFS Cf. A001358, A050508. Sequence in context: A035077 A032164 A177122 * A232170 A165570 A260117 Adjacent sequences:  A108537 A108538 A108539 * A108541 A108542 A108543 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jun 09 2005; revised Jun 13 2005 EXTENSIONS Corrected by T. D. Noe, Oct 25 2006 STATUS approved

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Last modified May 13 23:41 EDT 2021. Contains 343868 sequences. (Running on oeis4.)