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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 April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)