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Search: id:A005382
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| A005382 |
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Numbers n such that n and 2n-1 are primes.
(Formerly M0849)
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+0
55
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| 2, 3, 7, 19, 31, 37, 79, 97, 139, 157, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 661, 691, 727, 811, 829, 877, 937, 967, 997, 1009, 1069, 1171, 1237, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1657
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sequence gives values of n such sum(i=1,n,GCD(n,i))=A018804(n) is prime. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 25 2002
Let q = 2n-1. For these n (and q), the sum of two cyclotomic polynomials can be written as a product of cyclotomic polynomials and as a cyclotomic polynomial in x^2: Phi(q,x) + Phi(2q,x) = 2 Phi(n,x) Phi(2n,x) = 2 Phi(n,x^2). - T. D. Noe (noe(AT)sspectra.com), Nov 04 2003
Numbers n such that the n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime. {A005382} = {n such that A000384(n) is an element of A001358}. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 14 2006
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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].
J. Perry, Germain Primes
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FORMULA
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a(n) = A129521(n)/A005383(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 19 2007
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MAPLE
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f := proc(Q) local t1, i, j; t1 := []; for i from 1 to 500 do j := ithprime(i); if isprime(2*j-Q) then t1 := [op(t1), j]; fi; od: t1; end; f(1);
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MATHEMATICA
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Select[Prime[Range[300]], PrimeQ[2#-1]&]
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CROSSREFS
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Cf. A005383, A057326, A057327, A057328, A057329, A057330, A005603, A063908, A023204.
Cf. A000384, A001358.
Sequence in context: A074855 A038935 A073640 this_sequence A113165 A128025 A092064
Adjacent sequences: A005379 A005380 A005381 this_sequence A005383 A005384 A005385
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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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