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A245589 Primes which are the average of the two adjacent primes and also of the two adjacent squarefree numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 + 53))/2 = 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

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Last modified January 21 12:13 EST 2022. Contains 350477 sequences. (Running on oeis4.)