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A245589
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Primes which are the average of the two adjacent primes and also of the two adjacent squarefree numbers.
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1
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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PROG
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(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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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