The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A338262 Primes p such that the area of the triangle with sides p and the next two primes achieves a record for closeness to a prime. 2
 2, 3, 5, 239, 2521, 12239, 121421, 869657, 23638231, 30656909, 47964149, 48203291, 57273361, 552014783, 754751369, 941234383 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE a(3)=5 is in the sequence because 5 is a prime, the triangle with sides 5, 7, 11 has area 3*sqrt(299)/4 whose distance to the nearest prime, 13, is approximately 0.0313, and this is less than any distance previously achieved. MAPLE atr:= proc(p, q, r) local s; s:= (p+q+r)/2; sqrt(s*(s-p)*(s-q)*(s-r)) end proc: R:= 2, 3: p:= 3: q:= 5: r:= 7: count:= 2: dmin:= 7 - atr(3, 5, 7): while count < 8 do p:= q: q:= r: r:= nextprime(r); a:= atr(p, q, r); m:= round(a); if not isprime(m) then next fi; d:= abs(a-m); if is(d < dmin) then   count:= count+1;   dmin:= d;   R:= R, p; fi od: R; PROG (PARI) lista(nn) = {my(m=p=3, q=5, s, t); print1(2); forprime(r=7, nn, s=sqrt((p-s=(p+q+r)/2)*(q-s)*(s-r)*s); if(m>t=min(s-precprime(s), nextprime(s)-s), print1(", ", p); m=t); p=q; q=r); } \\ Jinyuan Wang, Oct 24 2020 CROSSREFS Cf. A330096, A338267, A338269. Sequence in context: A082755 A042067 A333803 * A042579 A033090 A303371 Adjacent sequences:  A338259 A338260 A338261 * A338263 A338264 A338265 KEYWORD nonn,more AUTHOR J. M. Bergot and Robert Israel, Oct 19 2020 EXTENSIONS a(10)-a(16) from Jinyuan Wang, Oct 24 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 10 22:11 EDT 2021. Contains 343780 sequences. (Running on oeis4.)