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 A254307 Least k such that there are n positive integers, all less than or equal to k, such that the sum of the reciprocals of their squares equals 1. 0
 6, 4, 6, 3, 4, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 8, 6, 6, 8, 6, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 9, 8, 8, 9, 8, 8, 9, 9, 8, 9, 9, 8, 9, 9, 9, 9, 10, 9, 9, 10, 9, 10, 10, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 COMMENTS a(2), a(3), and a(5) are undefined, so this sequence starts at offset 6. Gasarch (2015) shows that a(n) exists for all n >= 6, though this was known (folklore?) previously; he also poses three open questions. First occurrence of n: 1, 4, 9, 7, 25, 6, 49, 29, 53, 69, 121, 87, 140, 179, 221, ..., . - Robert G. Wilson v, Feb 15 2015 LINKS Bill Gasarch, The Solution to a problem in a Romanian math problem book (2015) FORMULA sqrt(n) <= a(n) < 2*sqrt(n) for n > 8. The lower bound is sharp since a(n^2) = n. EXAMPLE a(1) = 1: 1 = 1/1. a(4) = 2: 1 = 1/4 + 1/4 +1/4 + 1/4. a(6) = 6: 1 = 1/4 + 1/4 + 1/4 + 1/9 + 1/9 + 1/36. a(7) = 4: 1 = 1/4 + 1/4 + 1/4 + 1/16 + 1/16 + 1/16 + 1/16. a(8) = 6: 1 = 1/4 + 1/4 + 1/9 + 1/9 + 1/9 + 1/9 + 1/36 + 1/36. a(9) = 3: 1 = 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9. PROG (PARI) /* oo = 10^10; \\ uncomment for earlier pari versions */ ssd(n, total, mn, mx)=my(t, best=oo); if(total<=0, return(0)); if(n==1, return(if(issquare(1/total, &t)&&t>=mn&&t<=mx&&denominator(t)==1, t, 0))); for(k=mn, min(sqrtint(n\total), mx), t=ssd(n-1, total-1/k^2, k, mx); if(t, best=min(best, t))); best a(n)=my(k=sqrtint(n-1), t=oo); while(t==oo, k++; t=ssd(n-1, 1-1/k^2, 2, k)); k CROSSREFS Cf. A000058, A063664. Sequence in context: A201408 A153606 A086057 * A176394 A198235 A226294 Adjacent sequences:  A254304 A254305 A254306 * A254308 A254309 A254310 KEYWORD nonn AUTHOR Charles R Greathouse IV, Jan 27 2015 STATUS approved

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Last modified September 20 08:08 EDT 2019. Contains 327214 sequences. (Running on oeis4.)