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A214362 Arithmetic mean of next a(n) successive positive integers is prime.

%I A214362 #16 Jan 17 2017 22:28:01
%S A214362 3,3,1,7,5,7,5,11,1,7,5,7,9,3,9,11,5,3,1,7,5,23,1,19,9,11,1,3,17,23,1,
%T A214362 7,5,7,17,7,5,11,1,19,9,3,5,23,9,3,9,7,5,7,1,11,5,3,13,7,17,7,5,11,1,
%U A214362 7,17,7,9,11,13,27,5,7,5,11,9,3,9,7,5,3,1,23,1
%N A214362 Arithmetic mean of next a(n) successive positive integers is prime.
%C A214362 Corresponding primes: A062044(n).
%C A214362 All terms are odd. - _Robert Israel_, Jan 17 2017
%H A214362 Robert Israel, <a href="/A214362/b214362.txt">Table of n, a(n) for n = 1..10000</a>
%F A214362 a(n) = 2*(A062042(n)-A062042(n-1))+(-1)^n for n >= 2. - _Robert Israel_, Jan 17 2017
%e A214362 (1+2+3)/3 = 2 is prime, so a(1)=3,
%e A214362 then (4+5+6)/3 = 5 is prime, so a(2)=3,
%e A214362 then 7/1 = 7 is prime, so a(3)=1,
%e A214362 then (8+9+10+11+12+13+14)/7 = 11 is prime, so a(4)=7.
%p A214362 t:= 1:
%p A214362 for n from 1 to 100 do
%p A214362   for s from 1 by 2 do
%p A214362     if isprime((2*t + s - 1)/2) then
%p A214362       A[n]:= s; t:= t+s; break
%p A214362     fi
%p A214362 od od:
%p A214362 seq(A[n],n=1..100); # _Robert Israel_, Jan 17 2017
%o A214362 (PARI) firstTerms(n)={
%o A214362 my(k=1,j=1,x,y,a=vector(n));
%o A214362 while(j<=n,x=0;while(!isprime(k+x),x++);y=2*x+1;k+=y;a[j]=y;j++);
%o A214362 return(a)} \\ _R. J. Cano_, Jan 17 2017
%Y A214362 Cf. A000040, A062042, A062044, A213815.
%K A214362 nonn,easy
%O A214362 1,1
%A A214362 _Alex Ratushnyak_, Jul 18 2012