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 A339789 Odd primes p such that h(p) sets a record for closeness to the nearest integer, where h(p) is the altitude of a triangle with base p and other two sides the next two primes after p. 0
 3, 5, 7, 11, 249533, 290531, 350783, 935201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If q and r are the next two primes after p, h(p) = sqrt(2*(p^2*q^2+p^2*r^2+q^2*r^2)-p^4-q^4-r^4)/(2*p). LINKS EXAMPLE The first three odd primes are 3, 5, 7, 11, with h(3) ~= 4.330127020, h(5) ~= 5.187484941 (closer to 5 than h(3) is to 4), h(7) ~= 10.99976809 (closer to 11 than h(5) is to 5), h(11) ~= 12.99992053 (closer to 13 than h(7) is to 11).  Thus a(1) to a(4) are 3, 5, 7, 11.  After that the values are all farther from their nearest integers than h(11) is to 13 until 249533: h(249533) ~= 216109.99994158 is closer to 216110 than is h(11) to 13. MAPLE H:= (p, q, r) -> sqrt(2*(p^2*q^2+p^2*r^2+q^2*r^2)-p^4-q^4-r^4)/(2*p): q:= 3: r:= 5: bestw:= 1: R:= NULL: while r < 10^6 do   p:= q; q:= r; r:= nextprime(r);   v:= H(p, q, r);   w:= frac(v); w:= min(w, 1-w);   if is(w < bestw) then     bestw:= w;     R:= R, p;   fi; od: R; CROSSREFS Sequence in context: A262962 A321367 A121976 * A293598 A243179 A207459 Adjacent sequences:  A339786 A339787 A339788 * A339790 A339791 A339792 KEYWORD nonn,more AUTHOR J. M. Bergot and Robert Israel, Dec 16 2020 STATUS approved

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Last modified October 17 16:34 EDT 2021. Contains 348065 sequences. (Running on oeis4.)