A245589 Primes which are the average of the two adjacent primes and also of the two adjacent squarefree numbers.

53, 593, 1747, 2287, 4013, 4409, 5563, 6317, 8117, 10657, 10853, 11933, 12547, 12583, 12653, 15161, 16937, 17047, 17851, 18341, 19603, 19949, 20107, 22051, 26693, 31051, 32993, 35851, 35911, 39113, 42209, 42533, 44041, 46889, 47527, 48259, 50417, 51461

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 26 2014

Keywords

• nonn

Comments

Intersection of A006562 and A240475. Intersection of A006562 and A245289.

Examples

			53 is in this sequence because 53 = prime(16) = (prime(15) + prime(17))/2 = (47 + 59)/2 and 53 = squarefree(33) = (squarefree(32) + squarefree(34))/2 = (51 + 55)/2.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006562, A240475, A245289.

Programs

Maple

Primes:= select(isprime,[$1..10^5]):
Sqfree:= select(numtheory:-issqrfree,[$1..10^5]):
A:= NULL:
for i from 2 to nops(Primes)-1 do
   if Primes[i] = (Primes[i+1]+Primes[i-1])/2 then
      member(Primes[i],Sqfree,'j');
      if Primes[i] = (Sqfree[j-1]+Sqfree[j+1])/2 then
         A:= A,Primes[i]
      fi
   fi
od:
A; # Robert Israel, Aug 21 2014

PARI

maxp=60000;
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;
v = select(n->issquarefree(n), vector(maxp, n, n));
s=[]; for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], s=concat(s, v[k]))); s;
setintersect(p, s) \\ Colin Barker, Aug 07 2014

Extensions

Missing term (16937) inserted by Colin Barker, Aug 07 2014