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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
34
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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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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, December 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 A106879
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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njas
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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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