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 A293682 a(n) = least odd number k > 1 such that p = prime(n) is the middle of k consecutive primes which have arithmetic mean p, or 1 if no such k exists. 0
 1, 1, 3, 1, 1, 1, 7, 1, 1, 15, 1, 17, 1, 1, 1, 3, 1, 1, 1, 13, 1, 5, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 37, 1, 51, 17, 3, 1, 1, 3, 33, 1, 1, 7, 1, 1, 3, 1, 67, 7, 1, 1, 1, 1, 3, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 23, 37, 1, 3, 1, 35, 1, 13, 1, 13, 99, 11, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE There are no primes before prime(1) so a(1) = 1. a(3) = 3 as prime(3) = 5, which is the arithmetic mean of the three consecutive primes {3, 5, 7}. MAPLE P:=proc(x) local i, k, n, ok, p, pp, pn, q, s; for n from 1 to x do p:=ithprime(n); pp:=p; pn:=p; s:=p; q:=1; ok:=1; for i from 1 to n-1 do pp:=prevprime(pp); pn:=nextprime(pn); s:=s+pp+pn; q:=q+2; if p*q=s then print(q); ok:=0; break; fi; od; if ok=1 then print(1); fi; od; end: P(100); # Paolo P. Lava, Oct 19 2017 PROG (PARI) a(n) = {my(s = pprev = pnxt = p = prime(n), q=1); for(i=1, n-1, pprev = precprime(pprev - 1); pnxt = nextprime(pnxt + 1); s += (pprev + pnxt); q += 2; if(p * q == s, return(q))); return(1)} CROSSREFS Cf. A006562, A034964, A122535, A293395. Sequence in context: A102480 A157964 A140670 * A276651 A185587 A068845 Adjacent sequences:  A293679 A293680 A293681 * A293683 A293684 A293685 KEYWORD nonn AUTHOR David A. Corneth, Oct 14 2017 STATUS approved

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Last modified September 20 21:08 EDT 2019. Contains 327247 sequences. (Running on oeis4.)