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%I #21 Sep 03 2014 10:28:46
%S 53,593,1747,2287,4013,4409,5563,6317,8117,10657,10853,11933,12547,
%T 12583,12653,15161,16937,17047,17851,18341,19603,19949,20107,22051,
%U 26693,31051,32993,35851,35911,39113,42209,42533,44041,46889,47527,48259,50417,51461
%N Primes which are the average of the two adjacent primes and also of the two adjacent squarefree numbers.
%C Intersection of A006562 and A240475. Intersection of A006562 and A245289.
%H Jens Kruse Andersen, <a href="/A245589/b245589.txt">Table of n, a(n) for n = 1..10000</a>
%e 53 is in this sequence because 53 = prime(16) = (prime(15) + prime(17))/2 = (47 + 53))/2 = squarefree(33) = (squarefree(32) + squarefree(34))/2 = (51 + 55)/2.
%p Primes:= select(isprime,[$1..10^5]):
%p Sqfree:= select(numtheory:-issqrfree,[$1..10^5]):
%p A:= NULL:
%p for i from 2 to nops(Primes)-1 do
%p if Primes[i] = (Primes[i+1]+Primes[i-1])/2 then
%p member(Primes[i],Sqfree,'j');
%p if Primes[i] = (Sqfree[j-1]+Sqfree[j+1])/2 then
%p A:= A,Primes[i]
%p fi
%p fi
%p od:
%p A; # _Robert Israel_, Aug 21 2014
%o (PARI)
%o maxp=60000;
%o p=[]; my(v=primes(maxp)); for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], p=concat(p, v[k]))); p;
%o v = select(n->issquarefree(n), vector(maxp, n, n));
%o s=[]; for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], s=concat(s, v[k]))); s;
%o setintersect(p, s) \\ _Colin Barker_, Aug 07 2014
%Y Cf. A006562, A240475, A245289.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jul 26 2014
%E Missing term (16937) inserted by _Colin Barker_, Aug 07 2014
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