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A152050
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Smallest lower twin prime tp such that p + tp + 1 is prime. p ranges over the prime numbers.
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0
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3, 5, 3, 5, 3, 5, 3, 5, 11, 5, 3, 5, 3, 5, 5, 11, 5, 3, 11, 5, 3, 5, 11, 3, 5, 3, 5, 3, 17, 3, 5, 11, 11, 17, 5, 5, 3, 5, 5, 11, 11, 5, 3, 29, 11, 11, 3, 5, 3, 5, 11, 29, 5, 5, 5, 11, 5, 3, 11, 29, 17, 3, 5, 3, 29, 5, 11, 5, 3, 5, 29, 5, 5, 3, 5, 11, 3, 17, 11, 11, 11, 11, 5, 3, 5, 11, 3, 5, 3, 11
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OFFSET
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1,1
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COMMENTS
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Conjecture: For all primes p <= n there is always a lower twin prime L less than n such that p+L+1 is prime.
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LINKS
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EXAMPLE
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29 is the 9th odd prime. 29+3+1, 29+5+1 are not prime. 29+11+1 is prime, so a(9) = 11 the smallest lower twin prime satisfying the definition for prime 29.
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PROG
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(PARI) g(n) = ct=0; for(x=2, n, p1=prime(x); for(y=1, n, p2=twinl(y); z=p1+p2+1;
if(isprime(z), ct++; print1(p2", "); break))); ct
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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