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A063637
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Primes p such that p+2 is a semiprime.
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10
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2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127, 131, 139, 157, 167, 181, 199, 211, 233, 251, 257, 263, 293, 307, 317, 337, 353, 359, 379, 389, 401, 409, 443, 449, 467, 479, 487, 491, 499, 503, 509, 541, 557, 563, 571, 577, 587, 631, 647, 653, 677
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OFFSET
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1,1
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COMMENTS
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Primes of form p*q - 2, where p and q are primes.
Union of A049002 and A115093. - T. D. Noe, Mar 01 2006
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REFERENCES
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J.-R. Chen, On the representation of a large even integer as the sum of a prime and a product of at most two primes, Sci. Sinica 16 (1973), 157-176.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 146. [?Broken link]
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 146.
T. Tao, Obstructions to uniformity and arithmetic patterns in the primes
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FORMULA
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A010051(a(n)) * A064911(a(n) + 2) = 1. [Reinhard Zumkeller, Nov 15 2011]
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MATHEMATICA
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f[n_] := Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[ n]]; Select[ Prime[ Range[ 123]], f[ # + 2] == 2 &] (from Robert G. Wilson v, Apr 30 2005)
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PROG
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(PARI) { n=0; for (m=1, 10^9, p=prime(m); if (bigomega(p + 2) == 2, write("b063637.txt", n++, " ", p); if (n==1000, break)) ) } [From Harry J. Smith, Aug 26 2009]
(Haskell)
a063637 n = a063637_list !!(n-1)
a063637_list = filter ((== 1) . a064911 . (+ 2)) a000040_list
-- Reinhard Zumkeller, Nov 15 2011
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CROSSREFS
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Cf. A005383, A001358, A063638.
a(n) = A062721(n) - 2.
Cf. A109611 (Chen primes)
Sequence in context: A007821 A156007 A067774 * A216526 A020623 A109346
Adjacent sequences: A063634 A063635 A063636 * A063638 A063639 A063640
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Jul 21 2001
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STATUS
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approved
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