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

1,1

Comments

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

Links

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A006562, A240475, A245289.

Sequence in context: A165555 A201855 A112749 * A177141 A096707 A219989

Adjacent sequences: A245586 A245587 A245588 * A245590 A245591 A245592

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 26 2014

Extensions

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

Status

approved