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Search: id:A005383
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| A005383 |
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Numbers n such that both n and (n+1)/2 are primes.
(Formerly M2492)
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+0
38
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| 3, 5, 13, 37, 61, 73, 157, 193, 277, 313, 397, 421, 457, 541, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also, n such that sigma(n)/2 is prime. - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 10 2001; confirmed by Vladeta Jovovic, Dec 12, 2002.
Or, primes p such that p+1 is a semiprime. - Zak Seidov (zakseidov(AT)yahoo.com), Jul 01 2005
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
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a(n) = A129521(n)/A005382(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 19 2007
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MATHEMATICA
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A005383=Select[Prime[Range[1000]], Plus@@Last/@FactorInteger[ #+1]==2&] (Seidov)
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PROGRAM
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(Matlab) LIMIT = 8000 % Find all members of A005383 less than LIMIT A = primes(LIMIT); n = length(A); %n is number of primes less than LIMIT B = 2*A - 1; C = ones(n, 1)*A; %C is an n X n matrix, with C(i, j) = j-th prime D = B'*ones(1, n); %D is an n X n matrix, with D(i, j) = (ith prime)*2 - 1 [i, j] = find(C == D); A(j)
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CROSSREFS
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Cf. A005382, A057326, A057327, A057328, A057329, A057330, A005603.
Sequence in context: A027039 A032009 A032027 this_sequence A057188 A128548 A113606
Adjacent sequences: A005380 A005381 A005382 this_sequence A005384 A005385 A005386
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jan 18 2002
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