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A067076
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Numbers k such that 2*k + 3 is a prime.
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63
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0, 1, 2, 4, 5, 7, 8, 10, 13, 14, 17, 19, 20, 22, 25, 28, 29, 32, 34, 35, 38, 40, 43, 47, 49, 50, 52, 53, 55, 62, 64, 67, 68, 73, 74, 77, 80, 82, 85, 88, 89, 94, 95, 97, 98, 104, 110, 112, 113, 115, 118, 119, 124, 127, 130, 133, 134, 137, 139, 140, 145, 152, 154, 155
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OFFSET
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1,3
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COMMENTS
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The following sequences (allowing offset of first term) all appear to have the same parity: A034953, triangular numbers with prime indices; A054269, length of period of continued fraction for sqrt(p), p prime; A082749, difference between the sum of next prime(n) natural numbers and the sum of next n primes; A006254, numbers n such that 2n-1 is prime; A067076, 2n+3 is a prime. - Jeremy Gardiner, Sep 10 2004
n is in the sequence iff none of the numbers (n-3k)/(2k+1), 1 <= k <= (n-1)/5, is positive integer. - Vladimir Shevelev, May 31 2009
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LINKS
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FORMULA
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MAPLE
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select(t -> isprime(2*t+3), [$0..1000]); # Robert Israel, Feb 19 2015
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MATHEMATICA
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Select[Range[0, 200], PrimeQ[2#+3]&] (* Harvey P. Dale, Jun 10 2014 *)
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PROG
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(PARI) [k | k<-[0..99], isprime(2*k+3)] \\ for illustration
(Sage) [n for n in (0..200) if is_prime(2*n+3) ] # G. C. Greubel, May 21 2019
(GAP) Filtered([0..200], k-> IsPrime(2*k+3) ) # G. C. Greubel, May 21 2019
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CROSSREFS
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Numbers n such that 2n+k is prime: A005097 (k=1), this seq(k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19). - Jason Kimberley, Sep 07 2012
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Offset changed from 0 to 1 in 2008: some formulas here and elsewhere may need to be corrected.
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STATUS
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approved
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